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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: FRECHET:25</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 (  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st (  for <font color="Olive" title="b3">S</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b3">S</font> is  <a href="frechet.html#V2" title="FRECHET:attr.2">convergent</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> holds <br/> <a href="frechet.html#K2" title="FRECHET:func.2">Lim</a> <font color="Olive" title="b3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> ) holds <br/><font color="Olive" title="b2">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  ) holds <br/><font color="Olive" title="b1">T</font> is  <a href="frechet.html#V4" title="FRECHET:attr.4">sequential</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="frechet.html#T24" target="_self" onmouseover="rs('frechet/T24')" onmouseout="rh()">Th24</a></span>;<br/></div></div>
