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

<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:57_2_1"/>
<font color="Maroon">X</font> is <a href="tdlat_3.html#V3" target="_self">almost_discrete</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V3" target="_self">almost_discrete</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_2_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/><b>assume </b><a NAME="E1:57_2_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><a NAME="E2:57_2_1_1_1"/><b>then </b>
<font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:57_2_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T13" target="_self">Th13</a>, <a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:57_2_1_1"/>
<font color="Maroon">X0</font> is <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:57_2_1"/>
<font color="Maroon">X</font> is <a href="tdlat_3.html#V5" target="_self">hereditarily_extremally_disconnected</a>
 <b>by </b><i/>;<br/>


</div>
