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<b>let </b><font color="Maroon" title="c12">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">r</font>, <font color="Olive" title="b2">s</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <br/> for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c12">n</font></span>)</span> holds   <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b1">r</font>, <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Olive" title="b4">y</font>,<font color="Olive" title="b2">s</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c13">r</font>, <font color="Maroon" title="c14">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c12">n</font></span>)</span> holds   <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c13">r</font>, <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Olive" title="b2">y</font>,<font color="Maroon" title="c14">s</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c15">x</font>, <font color="Maroon" title="c16">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c12">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c15">x</font>,<font color="Maroon" title="c13">r</font>, <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c14">s</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> </span><br/>





<a NAME="E1:54"/>
(  <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c15">x</font>,<font color="Maroon" title="c13">r</font>, <a href="toprealb.html#K8" title="TOPREALB:func.8">Tunit_circle</a> <font color="Maroon" title="c12">n</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a>  &amp;  <a href="toprealb.html#K8" title="TOPREALB:func.8">Tunit_circle</a> <font color="Maroon" title="c12">n</font>, <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c14">s</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a>  )
 
<b>by </b><i><a class="txt" href="toprealb.html#E42"><i><font color="Green" title="E28">Lm15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:54"/>
 <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c15">x</font>,<font color="Maroon" title="c13">r</font>, <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c16">y</font>,<font color="Maroon" title="c14">s</font> <a href="borsuk_3.html#R2" title="BORSUK_3:pred.2">are_homeomorphic</a> 
 <b>by </b><i><a class="ref" href="borsuk_3.html#T3" title="BORSUK_3:th.3">BORSUK_3:3</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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