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<b>let </b><font color="Maroon">c<sub>12</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></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">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></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> <font color="Maroon">c<sub>12</sub></font></span>)</span>;<br/>





<a NAME="E1:54"/>
(  <a href="toprealb.html#K7" target="_self">Tcircle</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>, <a href="toprealb.html#K8" target="_self">Tunit_circle</a> <font color="Maroon">c<sub>12</sub></font> <a href="borsuk_3.html#R1">are_homeomorphic</a>  &amp;  <a href="toprealb.html#K8" target="_self">Tunit_circle</a> <font color="Maroon">c<sub>12</sub></font>, <a href="toprealb.html#K7" target="_self">Tcircle</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="borsuk_3.html#R1">are_homeomorphic</a>  )
 
<b>by </b><i><a class="txt" href="toprealb.html#E43"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:54"/>
 <a href="toprealb.html#K7" target="_self">Tcircle</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>, <a href="toprealb.html#K7" target="_self">Tcircle</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="borsuk_3.html#R1">are_homeomorphic</a> 
 <b>by </b><i><a class="ref" href="borsuk_3.html#T3">BORSUK_3:3</a></i>;<br/>


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