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<b>let </b><font color="Maroon" title="c1">X</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">x0</font>, <font color="Olive" title="b2">x1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">x0</font>,<font color="Olive" title="b2">x1</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  holds <br/> <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">x0</font>, <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">x1</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c2">x0</font>, <font color="Maroon" title="c3">x1</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x0</font>,<font color="Maroon" title="c3">x1</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  implies  <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font>, <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">x1</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>





<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">x0</font>,<font color="Maroon" title="c3">x1</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 ; <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> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font>, <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">x1</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<b>consider </b><font color="Maroon" title="c4">P</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c2">x0</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">h</font> =  <a href="topalg_1.html#K4" title="TOPALG_1:func.4">pi_1-iso</a> <font color="Maroon" title="c4">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="c1">X</font>,<font color="Maroon" title="c2">x0</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="c1">X</font>,<font color="Maroon" title="c3">x1</font></span>)</span> <b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="topalg_1.html#T51" target="_self" title="TOPALG_1:th.51">Th51</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="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"> <font color="Maroon" title="c5">h</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a></span><br/>

<b>thus </b><a NAME="E4:71"/>
<font color="Maroon" title="c5">h</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="topalg_1.html#T56" target="_self" title="TOPALG_1:th.56">Th56</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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