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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a>  &amp; <font color="Maroon" title="c1">S</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> implies <font color="Maroon" title="c2">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> )</span><br/>

<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a>  &amp; <font color="Maroon" title="c1">S</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a></span><br/>

<b>then consider </b><font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 <b>by </b><i><a class="ref" href="t_0topsp.html#D1" title="T_0TOPSP:def.1">T_0TOPSP:def 1</a></i>;<br/>
<a NAME="E4:25"/>
( <font color="Maroon" title="c3">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="txt" href="#E3:25"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon" title="c2">T</font> is <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>
 <b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="compts_1.html#T23" title="COMPTS_1:th.23">COMPTS_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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