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<b>let </b><font color="Maroon">c<sub>6</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="tsep_1.html#V1">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>



<b>assume </b><a NAME="E1:18"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="connsp_2.html#V1">locally_connected</a>
 ;<br/>

<a NAME="E2:18"/><b>then </b>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>7</sub></font> #) is <a href="connsp_2.html#V1">locally_connected</a>
 
<b>by </b><i><a class="txt" href="topalg_5.html#E24"><i><font color="Green">Lemma21</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:18"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="connsp_2.html#V1">locally_connected</a>
 <b>by </b><i><a class="ref" href="topalg_5.html#T12" target="_self">Th12</a></i>;<br/>


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