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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th61</font></span>: <a NAME="T61"><span class="comment"><font color="firebrick">:: TOPGEN_4:61</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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> holds <br/> (  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="topgen_4.html#K1" title="TOPGEN_4:func.1">TotFam</a> <font color="Olive" title="b1">T</font></span>)</span> is  <a href="topgen_4.html#V1" title="TOPGEN_4:attr.1">all-open-containing</a>  &amp;  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="topgen_4.html#K1" title="TOPGEN_4:func.1">TotFam</a> <font color="Olive" title="b1">T</font></span>)</span> is  <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a>  &amp;  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="topgen_4.html#K1" title="TOPGEN_4:func.1">TotFam</a> <font color="Olive" title="b1">T</font></span>)</span> is  <a href="topgen_4.html#V3" title="TOPGEN_4:attr.3">closed_for_countable_unions</a>  )</div></div>
