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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: FINTOPO4:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">FT</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">IT</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">FT</font>  st <font color="Olive" title="b1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  holds <br/>( <font color="Olive" title="b2">IT</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  iff  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">FT</font>  st <font color="Olive" title="b2">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">B</font> &amp; <font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</font> <a href="fintopo4.html#R1" title="FINTOPO4:pred.1">are_separated</a>  &amp;  not <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">IT</font> holds <br/><font color="Olive" title="b4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">IT</font> )</div></div>
