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<b>let </b><font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c2">S1</font>, <font color="Maroon" title="c3">S2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</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">S1</font>,<font color="Maroon" title="c3">S2</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a>  &amp; <font color="Maroon" title="c2">S1</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c3">S2</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c2">S1</font>,<font color="Maroon" title="c3">S2</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> 
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c2">S1</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">S2</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font></span><br/>

<b>consider </b><font color="Maroon" title="c4">G</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">S1</font>,<font color="Maroon" title="c3">S2</font><b> such that </b><br/><a NAME="E4:13"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c4">G</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 <b>by </b><i><a class="txt" href="waybel25.html#E1:13"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="t_0topsp.html#D1" title="T_0TOPSP:def.1">T_0TOPSP:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">H</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E6:13"/><i><font color="Green" title="E11">A4</font></i>: 
<font color="Maroon" title="c5">H</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>and </b><br/><a NAME="E7:13"/><i><font color="Green" title="E12">A5</font></i>: 
<font color="Maroon" title="c5">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">H</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">H</font>
 <b>and </b><br/><a NAME="E8:13"/><i><font color="Green" title="E13">A6</font></i>: 
 <a href="waybel18.html#K7" title="WAYBEL18:func.7">Image</a> <font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c2">S1</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> 
 <b>by </b><i><a class="txt" href="waybel25.html#E2:13"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="waybel18.html#D8" title="WAYBEL18:def.8">WAYBEL18:def 8</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">H</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel18.html#D8" title="WAYBEL18:def.8">WAYBEL18:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">H</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c5">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">H</font> &amp;  <a href="waybel18.html#K7" title="WAYBEL18:func.7">Image</a> <font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">S2</font> <a href="t_0topsp.html#R1" title="T_0TOPSP:pred.1">are_homeomorphic</a>  )</span><br/>

<b>consider </b><font color="Maroon" title="c6">F</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K7" title="WAYBEL18:func.7">Image</a> <font color="Maroon" title="c5">H</font></span>)</span>,<font color="Maroon" title="c2">S1</font><b> such that </b><br/><a NAME="E10:13"/><i><font color="Green" title="E14">A7</font></i>: 
<font color="Maroon" title="c6">F</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 <b>by </b><i><a class="txt" href="waybel25.html#E8:13"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="t_0topsp.html#D1" title="T_0TOPSP:def.1">T_0TOPSP:def 1</a></i>;<br/>
<a NAME="E11:13"/>
<font color="Maroon" title="c4">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">F</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 
<b>by </b><i><a class="txt" href="waybel25.html#E4:13"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="waybel25.html#E10:13"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="tops_2.html#T71" title="TOPS_2:th.71">TOPS_2:71</a></i>;<br/>
<b>hence </b><a NAME="E12:13"/>
( <font color="Maroon" title="c5">H</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c5">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">H</font> &amp;  <a href="waybel18.html#K7" title="WAYBEL18:func.7">Image</a> <font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c3">S2</font> <a href="t_0topsp.html#R1" title="T_0TOPSP:pred.1">are_homeomorphic</a>  )
 <b>by </b><i><a class="txt" href="waybel25.html#E6:13"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="waybel25.html#E7:13"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="t_0topsp.html#D1" title="T_0TOPSP:def.1">T_0TOPSP:def 1</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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