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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="tdlat_3.html#V3">almost_discrete</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="tsep_1.html#V1">open</a> <a href="tex_2.html#V2">proper</a> <a href="tex_3.html#V1" target="_self">dense</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>



<b>consider </b><font color="Maroon">X2</font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a> <a href="tex_2.html#V2">proper</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:90"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">X1</font>,<font color="Maroon">X2</font> <a href="tsep_2.html#R4">constitute_a_decomposition</a> 
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">X2</font> = <font color="Maroon">X2</font> as  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a> <a href="borsuk_1.html#V1">closed</a> <a href="tex_3.html#V3" target="_self">boundary</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> <b>by </b><i>, <a class="txt" href="tex_3.html#E3"><i><font color="Green">Lemma18</font></i></a>, <a class="ref" href="tsep_2.html#T35">TSEP_2:35</a></i>;<br/>
<b>take </b>
<font color="Maroon">X2</font>
;<br/>

<b>thus </b><a NAME="E4:90"/>
<font color="Maroon">X1</font>,<font color="Maroon">X2</font> <a href="tsep_2.html#R4">constitute_a_decomposition</a> 
 <b>by </b><i/>;<br/>


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