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<b>let </b><font color="Maroon" title="c6">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="c7">S</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="c6">T</font>;<br/><b>let </b><font color="Maroon" title="c8">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">T</font>;<br/><b>let </b><font color="Maroon" title="c9">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">S</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">B</font>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c8">A</font> is <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a>
 ;<br/>

<a NAME="E3:13"/>
<font color="Maroon" title="c6">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">S</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">B</font>
 
<b>by </b><i><a class="txt" href="topalg_5.html#E1:13"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="topalg_5.html#T4" target="_self" title="TOPALG_5:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E4:13"/>
<font color="Maroon" title="c7">S</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c9">B</font> is <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a>
 <b>by </b><i><a class="txt" href="topalg_5.html#E2:13"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="connsp_2.html#D6" title="CONNSP_2:def.6">CONNSP_2:def 6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_2.html#D6" title="CONNSP_2:def.6">CONNSP_2:def 6</a><br/>


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