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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: JORDAN21:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a><br/>  for <font color="Olive" title="b2">P</font> being   <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">C</font> &amp;  <a href="pscomp_1.html#K18" title="PSCOMP_1:func.18">W-min</a> <font color="Olive" title="b1">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp;  <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">E-max</a> <font color="Olive" title="b1">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp;  not  <a href="jordan6.html#K8" title="JORDAN6:func.8">Upper_Arc</a> <font color="Olive" title="b1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font> holds <br/> <a href="jordan6.html#K9" title="JORDAN6:func.9">Lower_Arc</a> <font color="Olive" title="b1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font></div></div>
