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<b>let </b><font color="Maroon">r</font> be  <a href="xxreal_0.html#V2">positive</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">o</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>;<br/>





<a NAME="E1:48"/>
 <a href="toprealb.html#K8">Tunit_circle</a> 2 <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K7">Tcircle</a> <span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>,1
 
<b>by </b><i><a class="ref" href="toprealb.html#D7">TOPREALB:def 7</a></i>;<br/>
<a NAME="E2:48"/><b>then </b>
 <a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">o</font>,<font color="Maroon">r</font>, <a href="toprealb.html#K8">Tunit_circle</a> 2 <a href="borsuk_3.html#R2">are_homeomorphic</a> 
 
<b>by </b><i><a class="ref" href="toprealb.html#T20">TOPREALB:20</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
 <a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p1">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> , <a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>,<font color="Maroon">x</font> <a href="group_6.html#R2">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="topalg_3.html#T35">TOPALG_3:35</a></i>;<br/>
<b>then consider </b><font color="Maroon">h</font> being   <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> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p2">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>,<font color="Maroon">x</font></span>)</span><b> such that </b><br/><a NAME="E5:48"/><i><font color="Green">E72</font></i>: 
<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#D15">GROUP_6:def 15</a></i>;<br/>
<b>take </b>
<font color="Maroon">h</font> <a href="group_6.html#K8">*</a> <a href="topalg_5.html#K8" target="_self">Ciso</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15">GROUP_6:def 15</a><br/>

<b>thus </b><a NAME="E6:48"/>
<font color="Maroon">h</font> <a href="group_6.html#K8">*</a> <a href="topalg_5.html#K8" target="_self">Ciso</a>  is <a href="group_6.html#V4">being_isomorphism</a>
 <b>by </b><i>, , <a class="ref" href="group_6.html#T74">GROUP_6:74</a></i>;<br/>


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