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<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/>

<b>assume </b><a NAME="E1:59_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">X0</font> is <a href="tsep_1.html#V1">open</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A0</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/><b>assume </b><a NAME="E1:59_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A0</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/><a NAME="E2:59_1_1_1"/>
<font color="Maroon">A0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 ;<br/><b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E4:59_1_1_1"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, , <a class="ref" href="tsep_1.html#T17">TSEP_1:17</a></i>;<br/><a NAME="E5:59_1_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
 <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="txt" href="tdlat_3.html#E1:59_1_1"><i><font color="Green">E21</font></i></a></i>;<br/><a NAME="E6:59_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A0</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X0</font></span>)</span>
 <b>by </b><i><a class="ref" href="pre_topc.html#T47">PRE_TOPC:47</a></i>;<br/><b>hence </b><a NAME="E7:59_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A0</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T14" target="_self">Th14</a>, <a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:59_1_1"/>
<font color="Maroon">X0</font> is <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a>
 <b>by </b><i><a class="txt" href="tdlat_3.html#E1:59_1_1"><i><font color="Green">E21</font></i></a></i>;<br/>


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