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<b>consider </b><font color="Maroon" title="c1">X</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>
<b>take </b>
<font color="Maroon" title="c1">X</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V5" title="TDLAT_3:attr.5">hereditarily_extremally_disconnected</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> )</span><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" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X0</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a></span><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" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> implies  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )</span><br/><b>assume </b><a NAME="E1:56_1_1_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a></span><br/><a NAME="E2:56_1_1_1_1"/>
<font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T18" target="_self" title="TDLAT_3:th.18">Th18</a></i>;<br/><b>hence </b><a NAME="E3:56_1_1_1_1"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="tdlat_3.html#E1:56_1_1_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="pre_topc.html#T52" title="PRE_TOPC:th.52">PRE_TOPC:52</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E2:56_1_1_1"/>
<font color="Maroon" title="c2">X0</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#D4" target="_self" title="TDLAT_3:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:56_1_1"/>
( <font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V5" title="TDLAT_3:attr.5">hereditarily_extremally_disconnected</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> )
 <b>by </b><i><a class="ref" href="tdlat_3.html#D5" target="_self" title="TDLAT_3:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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