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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: TOPDIM_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st <font color="Olive" title="b2">T</font> is  <a href="pre_topc.html#V9" title="PRE_TOPC:attr.9">regular</a>  holds <br/>( ( <font color="Olive" title="b2">T</font> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <font color="Olive" title="b2">T</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) iff  for <font color="Olive" title="b3">A</font> being   <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b4">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">T</font>  st  not <font color="Olive" title="b4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">A</font> holds <br/> ex <font color="Olive" title="b5">L</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">T</font> st <br/>( <font color="Olive" title="b5">L</font> <a href="metrizts.html#R2" title="METRIZTS:pred.2">separates</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<font color="Olive" title="b3">A</font> &amp; <font color="Olive" title="b5">L</font> is  <a href="topdim_1.html#NV2" title="TOPDIM_1:NV.2">finite-ind</a>  &amp;  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <font color="Olive" title="b5">L</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 ) )</div></div>
