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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>assume </b><a NAME="E1:7_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="group_1.html#V6">finite</a>  <a href="pre_topc.html#L1">TopStruct</a>  ;<br/>
<a NAME="E3:7_1_1"/>
 <a href="waybel23.html#K2">weight</a> <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="topgen_2.html#D4">TOPGEN_2:def 4</a></i>;<br/>
<a NAME="E4:7_1_1"/><b>then </b>
 <a href="waybel23.html#K2">weight</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K3">alef</a> 0
 
<b>by </b><i><a class="ref" href="card_4.html#T9">CARD_4:9</a></i>;<br/>
<a NAME="E5:7_1_1"/><b>then </b>
 <a href="waybel23.html#K2">weight</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K3">alef</a> 0
 
<b>by </b><i><a class="ref" href="card_1.html#T13">CARD_1:13</a></i>;<br/>
<b>hence </b><a NAME="E6:7_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel23.html#V5">second-countable</a>
 <b>by </b><i><a class="ref" href="waybel23.html#D6">WAYBEL23:def 6</a>, <a class="ref" href="card_1.html#T84">CARD_1:84</a>, <a class="ref" href="card_1.html#T38">CARD_1:38</a></i>;<br/>


</div>
