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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>let </b><font color="Maroon">B</font> be   <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" target="_self">modified_with_respect_to</a> <font color="Maroon">A</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:109"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:109"/><b>then </b>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="tmap_1.html#K5" target="_self">-extension_of_the_topology_of</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E3:109"/><b>then </b>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="tmap_1.html#K6" target="_self">modified_with_respect_to</a> <font color="Maroon">A</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E4:109"/>
<font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>


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