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<div><span class="kw">theorem </span><a NAME="T68"><span class="comment"><font color="firebrick">:: FINTOPO8:68</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">NT</font> being   <a href="fintopo8.html#V4" title="FINTOPO8:attr.4">normal</a>  <a href="fintopo8.html#NM1" title="FINTOPO8:NM.1">NTopSpace</a><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="fintopo8.html#V2" title="FINTOPO8:attr.2">closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">NT</font>  st <font color="Olive" title="b2">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">B</font> holds <br/> ex <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">NT</font>,<a href="fintopo8.html#K13" title="FINTOPO8:func.13">FMT_R^1</a> st <br/>( <font color="Olive" title="b4">F</font> is  <a href="fintopo8.html#V1" title="FINTOPO8:attr.1">continuous</a>  &amp; (  for <font color="Olive" title="b5">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">NT</font> holds <br/> (  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> &amp; <font color="Olive" title="b4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp; ( <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> implies <font color="Olive" title="b4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  ) &amp; ( <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">B</font> implies <font color="Olive" title="b4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) ) ) )</div></div>
