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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: C0SP3:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="c0sp3.html#NM1" title="C0SP3:NM.1">NormedLinearTopSpace</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">V</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b3">x</font> iff  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; <span class="p1"> { <span class="default"> <font color="Olive" title="b5">y</font> where <font color="Olive" title="b5">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font> : <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">y</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b3">x</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">r</font> </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> ) )</div></div>
