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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th11</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: FINTOPO7:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">ET</font> being   <a href="fintopo7.html#NM3" title="FINTOPO7:NM.3">FMT_TopSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">ET</font><br/>  for <font color="Olive" title="b3">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">ET</font> holds <br/> ( <font color="Olive" title="b3">V</font> is    <a href="fintopo7.html#M2" title="FINTOPO7:mode.2">a_neighborhood</a> of <font color="Olive" title="b2">A</font> iff  ex <font color="Olive" title="b4">O</font> being   <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">ET</font> st <br/>( <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">O</font> &amp; <font color="Olive" title="b4">O</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">V</font> ) )</div></div>
