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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: TOPS_5:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">S</font> being   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">S</font> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="t_0topsp.html#V1" title="T_0TOPSP:attr.1">open</a>  iff  ex <font color="Olive" title="b4">B</font> being   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Olive" title="b1">T</font> st <br/> for <font color="Olive" title="b5">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b5">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">B</font> holds <br/><font color="Olive" title="b3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b5">V</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )</div></div>
