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

<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="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c6">T</font>;<br/>



<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c6">T</font> is <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a>
 ;<br/>

<a NAME="E2:17"/><b>then </b>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">S</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">S</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#E24"><i><font color="Green" title="E21">Lm10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:17"/>
<font color="Maroon" title="c7">S</font> is <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a>
 <b>by </b><i><a class="ref" href="topalg_5.html#T12" target="_self" title="TOPALG_5:th.12">Th12</a></i>;<br/>


</div>
