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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/>

<b>assume </b><a NAME="E2:62"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">A</font> is <a href="tops_1.html#V1">dense</a>
 ;<br/>

<b>set </b><font color="Maroon">Z</font> = <font color="Maroon">X</font> <a href="tmap_1.html#K6">modified_with_respect_to</a> <font color="Maroon">A</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="tmap_1.html#K6">modified_with_respect_to</a> <font color="Maroon">A</font></span>)</span> <b>by </b><i><a class="ref" href="tmap_1.html#T104">TMAP_1:104</a></i>;<br/><b>take </b><font color="Maroon">C</font> = <font color="Maroon">C</font>;<br/><b>thus </b><a NAME="E2:62_1"/>
( <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="tmap_1.html#K6">modified_with_respect_to</a> <font color="Maroon">A</font></span>)</span> &amp; <font color="Maroon">C</font> is <a href="tops_3.html#V1">everywhere_dense</a> )
 <b>by </b><i>, <a class="ref" href="tex_1.html#T5" target="_self">Th5</a>, , <a class="ref" href="tmap_1.html#T104">TMAP_1:104</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:62"/>
not <font color="Maroon">X</font> <a href="tmap_1.html#K6">modified_with_respect_to</a> <font color="Maroon">A</font> is <a href="tdlat_3.html#V3">almost_discrete</a>
 <b>by </b><i/>;<br/>


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