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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: BORSUK_4:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</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="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> holds <br/> <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>)</span>)</span> <a href="borsuk_3.html#R1" title="BORSUK_3:pred.1">are_homeomorphic</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_4.html#T40" target="_self" onmouseover="rs('borsuk_4/T40')" onmouseout="rh()">Th37</a>, <a class="ref" href="topreal1.html#T9" onmouseover="rs('topreal1/T9')" onmouseout="rh()">TOPREAL1:9</a></span>;<br/></div></div>
