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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="compts_1.html#V3">Hausdorff</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">S</font> be  <a href="yellow_8.html#V2" target="_self">irreducible</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D6" target="_self">YELLOW_8:def 6</a><br/>



<b>consider </b><font color="Maroon">d</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E2:30"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">d</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_2.html#D1">TEX_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">d</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> ;<br/>
<b>take </b>
<font color="Maroon">d</font>
;<br/>

<b>thus </b><a NAME="E4:30"/>
<font color="Maroon">d</font> <a href="yellow_8.html#R1" target="_self">is_dense_point_of</a> <font color="Maroon">S</font>
 <b>by </b><i>, </i>;<br/>

<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E5:30"/>
<font color="Maroon">p</font> <a href="yellow_8.html#R1" target="_self">is_dense_point_of</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E6:30"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:30"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
