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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th9</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: UNIFORM3:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">US</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="uniform3.html#NM1" title="UNIFORM3:NM.1">UniformSpace</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="uniform2.html#K12" title="UNIFORM2:func.12">FMT_induced_by</a> <font color="Olive" title="b1">US</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">S</font> is  <a href="fintopo7.html#V1" title="FINTOPO7:attr.1">open</a>  iff <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fintopo7.html#K4" title="FINTOPO7:func.4">Family_open_set</a> <span class="p1">(<span class="default"><a href="uniform2.html#K12" title="UNIFORM2:func.12">FMT_induced_by</a> <font color="Olive" title="b1">US</font></span>)</span> )</div></div>
