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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: FINTOPO8:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">NTX</font>, <font color="Olive" title="b2">NTY</font> being   <a href="fintopo8.html#NM1" title="FINTOPO8:NM.1">NTopSpace</a><br/>  for <font color="Olive" title="b3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">NTX</font><br/>  for <font color="Olive" title="b4">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">NTY</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">NTX</font>,<font color="Olive" title="b2">NTY</font>  st <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> holds <br/>( <font color="Olive" title="b5">f</font> <a href="fintopo8.html#R3" title="FINTOPO8:pred.3">is_continuous_at</a> <font color="Olive" title="b3">x</font> iff  for <font color="Olive" title="b6">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fintopo8.html#K1" title="FINTOPO8:func.1">U_FMT</a> <font color="Olive" title="b4">y</font>  ex <font color="Olive" title="b7">W</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fintopo8.html#K1" title="FINTOPO8:func.1">U_FMT</a> <font color="Olive" title="b3">x</font> st <font color="Olive" title="b5">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b7">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">V</font> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="fintopo8.html#E22"><span class="lab"><font color="Green" title="E13">Lm11</font></span></a>, <a class="txt" href="fintopo8.html#E36"><span class="lab"><font color="Green" title="E27">Lm25</font></span></a></span>;<br/></div></div>
