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

<b>let </b><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">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"> for <font color="Olive" title="b1">s</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Olive" title="b1">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Olive" title="b2">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c6">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Olive" title="b1">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c7">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>, <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>







<b>take </b>
 <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font> is <a href="group_6.html#V4" title="GROUP_6:attr.4">being_isomorphism</a></span><br/>

<b>thus </b><a NAME="E1:45"/>
 <a href="topalg_4.html#K13" title="TOPALG_4:func.13">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font> is <a href="group_6.html#V4" title="GROUP_6:attr.4">being_isomorphism</a>
 <b>by </b><i><a class="ref" href="topalg_4.html#T29" target="_self" title="TOPALG_4:th.29">Th29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
