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<div><span class="kw">theorem </span><a NAME="T43"><span class="comment"><font color="firebrick">:: WAYBEL25:43</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="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a>  <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a> holds   <a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> (<font color="Olive" title="b1">X</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Olive" title="b2">Y</font></span>)</span>) is   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Olive" title="b2">Y</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">X</font></div></div>
