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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c3">Z</font> = <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K6" title="TMAP_1:func.6">modified_with_respect_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><a NAME="E1:61_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K6" title="TMAP_1:func.6">modified_with_respect_to</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="tmap_1.html#T104" title="TMAP_1:th.104">TMAP_1:104</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">C</font> = <font color="Maroon" title="c2">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K6" title="TMAP_1:func.6">modified_with_respect_to</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span></span>)</span> ;<br/><b>take </b><font color="Maroon" title="c5">C</font> = <font color="Maroon" title="c4">C</font>;<br/><b>thus </b><a NAME="E3:61_1"/>
<font color="Maroon" title="c5">C</font> is <a href="tops_1.html#V3" title="TOPS_1:attr.3">nowhere_dense</a>
 <b>by </b><i><a class="txt" href="tex_1.html#E1:61"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="tex_1.html#T7" target="_self" title="TEX_1:th.7">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:61"/>
not <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K6" title="TMAP_1:func.6">modified_with_respect_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> is <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</a>
 <b>by </b><i><a class="ref" href="tex_1.html#D7" target="_self" title="TEX_1:def.7">Def7</a></i>;<br/>


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