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<b>let </b><font color="Maroon">T</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">T</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:35_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 ;<br/><b>let </b><font color="Maroon">G</font> be    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">p</font>;<br/><a NAME="E2:35_1"/><i><font color="Green">E22</font></i>: 
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/><a NAME="E3:35_1"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">G</font> &amp;  <a href="tops_1.html#K1">Int</a> <font color="Maroon">G</font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i>, <a class="ref" href="tops_1.html#T51">TOPS_1:51</a></i>;<br/><a NAME="E4:35_1"/><b>then </b>
<font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#T8" target="_self">Th8</a>, <a class="ref" href="pre_topc.html#D13">PRE_TOPC:def 13</a></i>;<br/><b>hence </b><a NAME="E5:35_1"/>
<font color="Maroon">G</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:35"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">G</font> being   <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">p</font>  holds <font color="Olive">G</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">G</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>assume </b><a NAME="E1:35_2"/>
( <font color="Maroon">G</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> )
 ;<br/><a NAME="E2:35_2"/><b>then </b>
<font color="Maroon">G</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:35_2"/>
<font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#T8" target="_self">Th8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="pre_topc.html#D13">PRE_TOPC:def 13</a></i>;<br/>


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