<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>4</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> as    <a href="hidden.html#M1">set</a>  ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ;<br/>
<i><font color="Green">E21</font></i>:  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> = 
 <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T19" target="_self">Th19</a></i>
;<br/>
<a NAME="E6:25"/><b>then </b><i><font color="Green">E22</font></i>: 
(  <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T29">FUNCT_2:29</a></i>;<br/>
<a NAME="E7:25"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 
;<br/>
<i><font color="Green">E24</font></i>:  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T19" target="_self">Th19</a></i>
;<br/>
<a NAME="E9:25"/><b>then </b><i><font color="Green">E25</font></i>: 
(  <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T29">FUNCT_2:29</a></i>;<br/>
<a NAME="E10:25"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
;<br/>
<a NAME="E11:25"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:25"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 
;<br/>
<a NAME="E13:25"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E10:25"><i><font color="Green">E26</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E14:25"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E15:25"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
;<br/>
<a NAME="E16:25"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="treal_1.html#E7:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E17:25"/><i><font color="Green">E31</font></i>: 
 <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="treal_1.html#E5:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="treal_1.html#E13:25"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T36">FUNCT_2:36</a></i>;<br/>
<a NAME="E18:25"/><i><font color="Green">E32</font></i>: 
 <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E8:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="treal_1.html#E16:25"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_2.html#T36">FUNCT_2:36</a></i>;<br/>
<a NAME="E19:25"/><i><font color="Green">E33</font></i>: 
 <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E20:25"/><i><font color="Green">E34</font></i>: 
 <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E21:25"/><i><font color="Green">E35</font></i>: 
 <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> is  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E22:25"/><i><font color="Green">E36</font></i>: 
 <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="treal_1.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="treal_1.html#T15" target="_self">Th15</a></i>;<br/>
<b>thus </b><a NAME="E23:25"/>
 <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 <b>by </b><i><a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E10:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="treal_1.html#E12:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="treal_1.html#E17:25"><i><font color="Green">E31</font></i></a>, <a class="txt" href="treal_1.html#E20:25"><i><font color="Green">E34</font></i></a>, <a class="txt" href="treal_1.html#E21:25"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>

<b>thus </b><a NAME="E24:25"/>
<span class="p1">(<span class="default"><a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="funct_2.html#R2">=</a>  <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span>
 <b>by </b><i><a class="txt" href="treal_1.html#E5:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="treal_1.html#E13:25"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T36">FUNCT_2:36</a></i>;<br/>

<b>thus </b><a NAME="E25:25"/>
 <a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 <b>by </b><i><a class="txt" href="treal_1.html#E7:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="treal_1.html#E15:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="treal_1.html#E18:25"><i><font color="Green">E32</font></i></a>, <a class="txt" href="treal_1.html#E19:25"><i><font color="Green">E33</font></i></a>, <a class="txt" href="treal_1.html#E22:25"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>

<b>thus </b><a NAME="E26:25"/>
<span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span></span>)</span> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="funct_2.html#R2">=</a>  <a href="treal_1.html#K3" target="_self">L[01]</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="treal_1.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="treal_1.html#E8:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="treal_1.html#E9:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="treal_1.html#E16:25"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_2.html#T36">FUNCT_2:36</a></i>;<br/>


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