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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: WAYBEL30:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a>   <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>  st  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Olive" title="b1">N</font></span>)</span> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  holds <br/>( <font color="Olive" title="b1">N</font> is  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a>  iff  for <font color="Olive" title="b2">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">N</font>,<font color="Olive" title="b1">N</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>  st <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Olive" title="b1">N</font> holds <br/><font color="Olive" title="b2">X</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )</div></div>
