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<b>let </b><font color="Maroon">X</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be  <a href="tsep_1.html#V1" target="_self">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  <a href="tsep_1.html#V1" target="_self">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>assume </b><a NAME="E1:26_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font>
 ;<br/><b>then reconsider </b><font color="Maroon">BB</font> = <font color="Maroon">B</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X1</font> <b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/><a NAME="E3:26_1"/>
<font color="Maroon">BB</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, <a class="txt" href="tsep_1.html#E2"><i><font color="Green">Lemma15</font></i></a></i>;<br/><a NAME="E4:26_1"/><b>then </b><i><font color="Green">E27</font></i>: 
 ex <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">A</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">A</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">BB</font> )
 <b>by </b><i><a class="ref" href="tops_2.html#T32">TOPS_2:32</a></i>;<br/><b>reconsider </b><font color="Maroon">C</font> =  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/><a NAME="E6:26_1"/>
<font color="Maroon">C</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="txt" href="tsep_1.html#E2"><i><font color="Green">Lemma15</font></i></a></i>;<br/><b>hence </b><a NAME="E7:26_1"/>
<font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tsep_1.html#T1" target="_self">Th1</a>, <a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:26"/>
<font color="Maroon">X2</font> is  <a href="tsep_1.html#V1" target="_self">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="tsep_1.html#E2"><i><font color="Green">Lemma15</font></i></a>, </i>;<br/>


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