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<b>let </b><font color="Maroon" title="c5">S</font>, <font color="Maroon" title="c6">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>;<br/><b>let </b><font color="Maroon" title="c7">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">S</font>;<br/><b>let </b><font color="Maroon" title="c8">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c6">T</font>;<br/><b>let </b><font color="Maroon" title="c9">f</font> be  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">T</font>;<br/><b>let </b><font color="Maroon" title="c10">P</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c8">t</font>,<font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">s</font>;<br/><b>let </b><font color="Maroon" title="c11">h</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c7">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c6">T</font>,<font color="Maroon" title="c8">t</font></span>)</span>;<br/>











<b>assume </b><a NAME="E1:42"/>
<font color="Maroon" title="c9">f</font> <a href="tops_2.html#NR1" title="TOPS_2:NR.1">is_homeomorphism</a> 
 ;<br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
 <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">s</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 
<b>by </b><i><a class="ref" href="topalg_3.html#T33" target="_self" title="TOPALG_3:th.33">Th33</a></i>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E3:42"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c8">t</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E4:42"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c11">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c10">P</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">s</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c12">G</font> =  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c10">P</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c6">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">s</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c6">T</font>,<font color="Maroon" title="c8">t</font></span>)</span> <b>by </b><i><a class="txt" href="topalg_3.html#E3:42"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="topalg_1.html#T51" title="TOPALG_1:th.51">TOPALG_1:51</a></i>;<br/>
<a NAME="E6:42"/>
<font color="Maroon" title="c12">G</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E3:42"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="topalg_1.html#T56" title="TOPALG_1:th.56">TOPALG_1:56</a></i>;<br/>
<b>hence </b><a NAME="E7:42"/>
<font color="Maroon" title="c11">h</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="topalg_3.html#E2:42"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="topalg_3.html#E4:42"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="group_6.html#T74" title="GROUP_6:th.74">GROUP_6:74</a></i>;<br/>


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