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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:39"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<a NAME="E3:39"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2" target="_self">connected</a>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E1:39"><i><font color="Green">E32</font></i></a>, <a class="ref" href="connsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E4:39"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2" target="_self">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E1:39"><i><font color="Green">E32</font></i></a>, <a class="txt" href="connsp_1.html#E2:39"><i><font color="Green">E33</font></i></a>, <a class="ref" href="connsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>


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