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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="E1:8"/>
( <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a> or <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> )
 ;<br/>

<a NAME="E2:8"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="tex_4.html#T58">TEX_4:58</a>, <a class="ref" href="tex_4.html#T62">TEX_4:62</a></i>;<br/>
<b>assume </b><a NAME="E3:8"/>
<font color="Maroon">A</font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 ;<br/>

<a NAME="E4:8"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:8"/>
not <font color="Maroon">A</font> is <a href="tex_2.html#V1">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#T5">TEX_2:5</a></i>;<br/>


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