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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: TOPMETR:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">Y</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b3">K0</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</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">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b3">K0</font></span>)</span>,<font color="Olive" title="b2">Y</font>  st <font color="Olive" title="b4">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <font color="Olive" title="b3">K0</font> holds <br/><font color="Olive" title="b5">g</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> </div></div>
