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<b>let </b><font color="Maroon" title="c3">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">Z</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">T</font>;<br/><b>let </b><font color="Maroon" title="c5">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">T</font>;<br/><b>let </b><font color="Maroon" title="c6">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">Z</font>;<br/><b>let </b><font color="Maroon" title="c7">N</font> be  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c5">t</font>;<br/><b>let </b><font color="Maroon" title="c8">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">Z</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">z</font>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">N</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">Z</font></span>)</span>
 ;<br/>

<a NAME="E3:31"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c5">t</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="c7">N</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/>
<a NAME="E4:31"/><i><font color="Green" title="E17">A4</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">N</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44" title="TOPS_1:th.44">TOPS_1:44</a></i>;<br/>
<a NAME="E5:31"/>
<font color="Maroon" title="c8">M</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="topreala.html#E2:31"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></i>;<br/>
<a NAME="E6:31"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">M</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T55" title="TOPS_1:th.55">TOPS_1:55</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<font color="Maroon" title="c6">z</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="c8">M</font>
 
<b>by </b><i><a class="txt" href="topreala.html#E1:31"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="topreala.html#E2:31"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="topreala.html#E3:31"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="topreala.html#E4:31"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:31"/>
<font color="Maroon" title="c8">M</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c6">z</font>
 <b>by </b><i><a class="txt" href="topreala.html#E2:31"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></i>;<br/>


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