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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: JORDAN5A:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( <font color="Olive" title="b1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pcomps_1.html#K2" title="PCOMPS_1:func.2">Family_open_set</a> <a href="metric_1.html#K7" title="METRIC_1:func.7">RealSpace</a> iff <font color="Olive" title="b1">X</font> is  <a href="rcomp_1.html#V3" title="RCOMP_1:attr.3">open</a>  ) <span class="kw">by</span> <span class="lab"><a class="txt" href="jordan5a.html#E7"><span class="lab"><font color="Green" title="E6">Lm3</font></span></a>, <a class="txt" href="jordan5a.html#E8"><span class="lab"><font color="Green" title="E7">Lm4</font></span></a></span>;<br/></div></div>
