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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="borsuk_4.html#K1" target="_self">I(01)</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> <b> such that </b><a NAME="E1:70"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="rcomp_1.html#K1">.]</a></span> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <a href="borsuk_4.html#K1" target="_self">I(01)</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font> as    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="ref" href="tsep_1.html#T7">TSEP_1:7</a></i>;<br/>
<a NAME="E3:70"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T86">BORSUK_1:86</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> as    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="topmetr.html#K5">I[01]</a>  <b>by </b><i><a class="txt" href="borsuk_4.html#E1:70"><i><font color="Green">E60</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="treal_1.html#T6">TREAL_1:6</a></i>;<br/>
<a NAME="E5:70"/><i><font color="Green">E61</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E1:70"><i><font color="Green">E60</font></i></a>, <a class="ref" href="topmetr.html#T25">TOPMETR:25</a></i>;<br/>
<a NAME="E6:70"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E7:70"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E5:70"><i><font color="Green">E61</font></i></a>, <a class="ref" href="tsep_1.html#T5">TSEP_1:5</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="treal_1.html#K2">(#)</a> </span>)</span>;<br/>
<a NAME="E8:70"/>
 <a href="treal_1.html#K3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1">(#)</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="treal_1.html#K2">(#)</a> </span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E1:70"><i><font color="Green">E60</font></i></a>, <a class="ref" href="treal_1.html#T20">TREAL_1:20</a></i>;<br/>
<b>hence </b><a NAME="E9:70"/>
 <a href="topmetr.html#K5">I[01]</a> ,<a href="borsuk_4.html#K1" target="_self">I(01)</a>  <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>1</sub></font> <a href="t_0topsp.html#R1">are_homeomorphic</a> 
 <b>by </b><i><a class="txt" href="borsuk_4.html#E7:70"><i><font color="Green">E62</font></i></a>, <a class="ref" href="topmetr.html#T27">TOPMETR:27</a>, <a class="ref" href="t_0topsp.html#D1">T_0TOPSP:def 1</a></i>;<br/>


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