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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th35</font></span>: <a NAME="T35"><span class="comment"><font color="firebrick">:: YELLOW_9:35</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">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><br/>  for <font color="Olive" title="b3">K</font> being   <a href="cantor_1.html#NM2" title="CANTOR_1:NM.2">prebasis</a> of <font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font> holds <br/> ( <font color="Olive" title="b4">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  iff  for <font color="Olive" title="b5">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">T</font>  st <font color="Olive" title="b5">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">K</font> holds <br/><font color="Olive" title="b4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )</div></div>
