<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: FRECHET2:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st <font color="Olive" title="b1">T</font> is  <a href="frechet.html#V4" title="FRECHET:attr.4">sequential</a>  holds <br/>( <font color="Olive" title="b1">T</font> is  <a href="frechet.html#V3" title="FRECHET:attr.3">Frechet</a>  iff  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font> holds <br/> (  <a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <font color="Olive" title="b2">A</font> &amp;  <a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <font color="Olive" title="b3">B</font></span>)</span> &amp;  <a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <span class="p1">(<span class="default"><a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="frechet2.html#K1" title="FRECHET2:func.1">Cl_Seq</a> <font color="Olive" title="b2">A</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="frechet2.html#T21" target="_self" onmouseover="rs('frechet2/T21')" onmouseout="rh()">Th21</a>, <a class="ref" href="frechet2.html#T22" target="_self" onmouseover="rs('frechet2/T22')" onmouseout="rh()">Th22</a></span>;<br/></div></div>
