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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: CC0SP2:32</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">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><a href="cc0sp2.html#K5" title="CC0SP2:func.5">C_Normed_Algebra_of_ContinuousFunctions</a> <font color="Olive" title="b1">X</font></span>)</span>  st <font color="Olive" title="b2">seq</font> is  <a href="csspace3.html#V1" title="CSSPACE3:attr.1">CCauchy</a>  holds <br/><font color="Olive" title="b2">seq</font> is  <a href="clvect_1.html#V9" title="CLVECT_1:attr.9">convergent</a> </div></div>
