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<b>let </b><font color="Maroon">c<sub>8</sub></font> be  <a href="toprealb.html#V1">being_simple_closed_curve</a>  <a href="pre_topc.html#M1">SubSpace</a> of  <a href="euclid.html#K15">TOP-REAL</a> 2;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>8</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>10</sub></font> being  <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> , <font color="Maroon">c<sub>11</sub></font> being   <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>, <font color="Maroon">c<sub>12</sub></font> being   <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">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span>;<br/>
<a NAME="E2:49"/><i><font color="Green">E45</font></i>: 
 <a href="gr_cy_1.html#K3">INT.Group</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">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font> <a href="group_6.html#R2">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="topalg_5.html#E49"><i><font color="Green">Lemma43</font></i></a></i>;<br/>
<a NAME="E3:49"/>
 <a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="borsuk_3.html#R1">are_homeomorphic</a> 
 
<b>by </b><i><a class="ref" href="toprealb.html#T11">TOPREALB:11</a></i>;<br/>
<a NAME="E4:49"/><b>then </b>
 <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">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>, <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></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>hence </b><a NAME="E5:49"/>
 <a href="gr_cy_1.html#K3">INT.Group</a> , <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="group_6.html#R2">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="topalg_5.html#E2:49"><i><font color="Green">E45</font></i></a>, <a class="ref" href="group_6.html#T78">GROUP_6:78</a></i>;<br/>


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