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<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>;<br/>

<a NAME="E1:61_1_1"/>
for <font color="Olive" title="b1">Y</font> being 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="c2">X0</font> holds  <font color="Olive" title="b1">Y</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">Y</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="c2">X0</font>;<br/>

<a NAME="E1:61_1_1_1"/>
<font color="Maroon" title="c3">Y</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T7" title="TSEP_1:th.7">TSEP_1:7</a></i>;<br/>
<b>hence </b><a NAME="E2:61_1_1_1"/>
<font color="Maroon" title="c3">Y</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#D5" target="_self" title="TDLAT_3:def.5">Def5</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:61_1_1"/>
<font color="Maroon" title="c2">X0</font> is <a href="tdlat_3.html#V5" title="TDLAT_3:attr.5">hereditarily_extremally_disconnected</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#D5" target="_self" title="TDLAT_3:def.5">Def5</a></i>;<br/>


</div>
