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<b>let </b><font color="Maroon" title="c1">GX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E3:17"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="connsp_3.html#E1:17"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="connsp_1.html#T20" title="CONNSP_1:th.20">CONNSP_1:20</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="connsp_3.html#K1" title="CONNSP_3:func.1">Component_of</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="connsp_3.html#E1:17"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="connsp_3.html#E2:17"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="connsp_3.html#T13" target="_self" title="CONNSP_3:th.13">Th13</a>, <a class="ref" href="pre_topc.html#T48" title="PRE_TOPC:th.48">PRE_TOPC:48</a></i>;<br/>


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