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<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K3">R^1</a> ;<br/><b>let </b><font color="Maroon">N</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> ;<br/>





<b>assume </b><a NAME="E1:48"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font>
 ;<br/>

<b>given </b><font color="Maroon">r</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><a NAME="E2:48"/><i><font color="Green">E38</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E3:48"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rcomp_1.html#D7">RCOMP_1:def 7</a><br/>

<a NAME="E4:48"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">M</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, , <a class="ref" href="jordan6.html#T46">JORDAN6:46</a></i>;<br/>
<a NAME="E5:48"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , , <a class="ref" href="topreal6.html#T20">TOPREAL6:20</a></i>;<br/>
<b>hence </b><a NAME="E6:48"/>
<font color="Maroon">M</font> is    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="connsp_2.html#T5">CONNSP_2:5</a></i>;<br/>


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