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

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">ADD</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>  st ( for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">ADD</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f1</font> <a href="nagata_1.html#K3" title="NAGATA_1:func.3">+</a> <font color="Olive" title="b3">f2</font> ) holds <br/>for <font color="Olive" title="b2">map9</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b2">map9</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Olive" title="b1">ADD</font> holds <br/><font color="Olive" title="b2">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">ADD</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c2">ADD</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="nagata_1.html#K3" title="NAGATA_1:func.3">+</a> <font color="Olive" title="b2">f2</font> ) implies for <font color="Olive" title="b1">map9</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">map9</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">ADD</font> holds <br/><font color="Olive" title="b1">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:46"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c2">ADD</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="nagata_1.html#K3" title="NAGATA_1:func.3">+</a> <font color="Olive" title="b2">f2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">map9</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">map9</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">ADD</font> holds <br/><font color="Olive" title="b1">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">F</font> =  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">map9</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">map9</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">ADD</font> implies <font color="Maroon" title="c4">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:46"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c4">map9</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">ADD</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a> </span><br/>

<a NAME="E3:46"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:46_1"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> st <font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E3:46_1"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>
<a NAME="E4:46_1"/>
<font color="Maroon" title="c2">ADD</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">map9</font>,<font color="Maroon" title="c4">map9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">map9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="binop_1.html#T11" title="BINOP_1:th.11">BINOP_1:11</a></span>;<br/>
<a NAME="E5:46_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">map9</font> <a href="nagata_1.html#K3" title="NAGATA_1:func.3">+</a> <font color="Maroon" title="c4">map9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">map9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E26">A1</font></span></a></span>;<br/>
<a NAME="E6:46_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nagata_1.html#D7" target="_self" title="NAGATA_1:def.7">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:46_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46_1"><span class="lab"><font color="Green" title="E29">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">reconsider </span><font color="Maroon" title="c5">map99</font> = <font color="Maroon" title="c4">map9</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></span>;<br/>
<a NAME="E5:46"/>
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b1">A</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">mCla</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">A</font></span>)</span> or <font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:46_2"/>
<font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">A</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font></span>)</span></span><br/>

<a NAME="E2:46_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A5</font></span>: 
 ex <font color="Olive" title="b1">Cla</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">Cla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">map9</font> &amp; <font color="Olive" title="b1">Cla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c6">A</font> &amp; <font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">map99</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">Cla</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></span>;<br/>
<a NAME="E3:46_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T52" title="PRE_TOPC:th.52">PRE_TOPC:52</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:46_2"/><span class="lab"><font color="Green" title="E30">A6</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c8">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46_2"><span class="lab"><font color="Green" title="E30">A6</font></span></a></span>;<br/>
<a NAME="E7:46_2"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">map9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c4">map9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E8:46_2"/><span class="kw">then </span>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">map9</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46_2"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></span>;<br/>
<a NAME="E9:46_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A7</font></span>: 
<font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">map9</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E2:46_2"><span class="lab"><font color="Green" title="E29">A5</font></span></a></span>;<br/>
<a NAME="E10:46_2"/>
<font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T48" title="PRE_TOPC:th.48">PRE_TOPC:48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:46_2"/>
<font color="Maroon" title="c7">mCla</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">map99</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c6">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:46_2"><span class="lab"><font color="Green" title="E31">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:46"/><span class="kw">then </span>
<font color="Maroon" title="c5">map99</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#T57" title="TOPS_2:th.57">TOPS_2:57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:46"/>
<font color="Maroon" title="c4">map9</font> is  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal6.html#T83" title="TOPREAL6:th.83">TOPREAL6:83</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
