<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="topgrp_1.html#V3" title="TOPGRP_1:attr.3">UnContinuous</a> <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">A</font> being   <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> holds  <font color="Olive" title="b2">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Olive" title="b1">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being   <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> holds  <font color="Olive" title="b1">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span><br/>





<a NAME="E1:100"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:100"/><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c4">Q</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Q</font> )
 <b>by </b><i><a class="ref" href="tops_1.html#T54" title="TOPS_1:th.54">TOPS_1:54</a></i>;<br/>
<a NAME="E4:100"/>
( <font color="Maroon" title="c4">Q</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">Q</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Q</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a>  )
 
<b>by </b><i><a class="txt" href="topgrp_1.html#E3:100"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="topgrp_1.html#T9" target="_self" title="TOPGRP_1:th.9">Th9</a>, <a class="ref" href="topgrp_1.html#T51" target="_self" title="TOPGRP_1:th.51">Th51</a>, <a class="ref" href="group_2.html#T5" title="GROUP_2:th.5">GROUP_2:5</a></i>;<br/>
<b>hence </b><a NAME="E5:100"/>
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="group_2.html#K1" title="GROUP_2:func.1">"</a> </span>)</span>
 <b>by </b><i><a class="ref" href="tops_1.html#T54" title="TOPS_1:th.54">TOPS_1:54</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
