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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: BROUWER3:3</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">TM</font> being   <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>  st <font color="Olive" title="b2">TM</font> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp; <font color="Olive" title="b2">TM</font> is  <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a>  holds <br/> for <font color="Olive" title="b3">F</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">TM</font>  st  <a href="topdim_1.html#K2" title="TOPDIM_1:func.2">ind</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/> for <font color="Olive" title="b4">f</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">TM</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b3">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="toprealb.html#K8" title="TOPREALB:func.8">Tunit_circle</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>  ex <font color="Olive" title="b5">g</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">TM</font>,<span class="p1">(<span class="default"><a href="toprealb.html#K8" title="TOPREALB:func.8">Tunit_circle</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> st <font color="Olive" title="b5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font></div></div>
