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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: RUSUB_5:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K5" title="RUSUB_5:func.5">TopUnitSpace</a> <font color="Olive" title="b1">V</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">M</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  iff  for <font color="Olive" title="b3">v</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">M</font> holds <br/> ex <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>( <font color="Olive" title="b4">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_5.html#D5" target="_self" onmouseover="rs('rusub_5/D5')" onmouseout="rh()">Def5</a></span>;<br/></div></div>
