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<b>consider </b><font color="Maroon">X</font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a> <a href="tdlat_3.html#V1" target="_self">discrete</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_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="56_1_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="E1:56_1_1_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><a NAME="E2:56_1_1_1_1"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:56_1_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="E2:56_1_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="E3:56_1_1"/>
( <font color="Maroon">X</font> is <a href="tdlat_3.html#V5" target="_self">hereditarily_extremally_disconnected</a> &amp; <font color="Maroon">X</font> is <a href="pre_topc.html#V1">strict</a> )
 <b>by </b><i/>;<br/>


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