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<b>let </b><font color="Maroon">Y0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>;<br/>

<b>assume </b><a NAME="E1:50_1_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">Y0</font> is <a href="realset2.html#V3">trivial</a> &amp; <font color="Maroon">Y0</font> is <a href="pre_topc.html#V2">TopSpace-like</a> )
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E3:50_1_1"/><i><font color="Green">E22</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">Y0</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="tex_2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:50_1_1"/>
(  <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is <a href="realset2.html#V3">trivial</a> &amp;  <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is <a href="pre_topc.html#V2">TopSpace-like</a> )
 
<b>by </b><i><a class="txt" href="tex_2.html#E1:50_1_1"><i><font color="Green">E17</font></i></a>, , </i>;<br/>
<a NAME="E5:50_1_1"/><b>then </b>
(  <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is <a href="tdlat_3.html#V1">discrete</a> &amp;  <a href="tex_2.html#K1" target="_self">Sspace</a> <font color="Maroon">y</font> is <a href="tdlat_3.html#V2">anti-discrete</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:50_1_1"/>
( <font color="Maroon">Y0</font> is <a href="tdlat_3.html#V1">discrete</a> &amp; <font color="Maroon">Y0</font> is <a href="tdlat_3.html#V2">anti-discrete</a> )
 <b>by </b><i>, , </i>;<br/>


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