<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c3">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:30_1_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c3">S</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font>
 ;<br/><b>take </b><font color="Maroon" title="c4">N</font> =  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">S</font>;<br/><b>thus </b><a NAME="E2:30_1_1_1"/>
<font color="Maroon" title="c4">N</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ;<br/><b>thus </b><a NAME="E3:30_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font>
 <b>by </b><i><a class="txt" href="urysohn1.html#E1:30_1_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a></i>;<br/><b>thus </b><a NAME="E4:30_1_1_1"/>
<font color="Maroon" title="c4">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T44" title="TOPS_1:th.44">TOPS_1:44</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:30_1_1"/>
 ex <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">S</font> )
 ;<br/>

<b>hence </b><a NAME="E3:30_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T54" title="TOPS_1:th.54">TOPS_1:54</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a><br/>


</div>
