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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">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">U1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:7"/>
<font color="Maroon">U1</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:7"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">U1</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">V</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:7"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E5:7"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">U1</font>
 <b>and </b><br/><a NAME="E6:7"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T54">TOPS_1:54</a></i>;<br/>
<b>reconsider </b><font color="Maroon">V</font> = <font color="Maroon">V</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">V</font>
;<br/>

<b>thus </b><a NAME="E8:7"/>
( <font color="Maroon">V</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> &amp; <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">U1</font> )
 <b>by </b><i>, , , </i>;<br/>


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