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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">t</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">f</font> is <a href="tops_2.html#V3">being_homeomorphism</a>
 ;<br/>

<a NAME="E2:40"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">f</font>,<font color="Maroon">s</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 
<b>by </b><i/>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E3:40"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font>,<font color="Maroon">t</font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E4:40"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">h</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K4">pi_1-iso</a> <font color="Maroon">P</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">f</font>,<font color="Maroon">s</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon">G</font> =  <a href="topalg_1.html#K4">pi_1-iso</a> <font color="Maroon">P</font> as   <a href="group_6.html#NM2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t</font></span>)</span> <b>by </b><i>, <a class="ref" href="topalg_1.html#T51">TOPALG_1:51</a></i>;<br/>
<a NAME="E6:40"/>
<font color="Maroon">G</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 
<b>by </b><i>, <a class="ref" href="topalg_1.html#T56">TOPALG_1:56</a></i>;<br/>
<b>hence </b><a NAME="E7:40"/>
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i>, , <a class="ref" href="group_6.html#T74">GROUP_6:74</a></i>;<br/>


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