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

<b>thus </b><a NAME="E1:30_1_1"/>
 ex <font color="Olive">Un</font> being  <a href="nagata_1.html#NM1">FamilySequence</a> of <font color="Maroon">T</font> st <font color="Olive">Un</font> is <a href="nagata_1.html#V3" target="_self">sigma_locally_finite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">Un</font> being   <a href="nagata_1.html#NM1">FamilySequence</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E2:30_1_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">Un</font> is <a href="nagata_1.html#V2" target="_self">sigma_discrete</a>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">Un</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:30_1_1_1_1"/>
<font color="Maroon">Un</font> <a href="nagata_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> is <a href="nagata_1.html#V1" target="_self">discrete</a>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E2:30_1_1_1_1"/>
<font color="Maroon">Un</font> <a href="nagata_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> is <a href="pcomps_1.html#V1">locally_finite</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:30_1_1_1"/>
<font color="Maroon">Un</font> is <a href="nagata_1.html#V3" target="_self">sigma_locally_finite</a>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>


</div>
