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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: CC0SP2:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="cc0sp1.html#K7" title="CC0SP1:func.7">C_Normed_Algebra_of_BoundedFunctions</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font></span>)</span>  st <font color="Olive" title="b2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cc0sp2.html#K2" title="CC0SP2:func.2">CContinuousFunctions</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b2">Y</font> is  <a href="ncfcont1.html#V2" title="NCFCONT1:attr.2">closed</a> </div></div>
