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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:14"/>
<font color="Maroon" title="c1">T</font> is <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a>
 ;<br/>

<a NAME="E2:14"/><b>then </b><i><font color="Green" title="E6">A1</font></i>: 
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="ref" href="waybel23.html#D6" title="WAYBEL23:def.6">WAYBEL23:def 6</a></i>;<br/>
<a NAME="E3:14"/>
 <a href="topgen_1.html#K4" title="TOPGEN_1:func.4">density</a> <font color="Maroon" title="c1">T</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="topgen_4.html#T5" target="_self" title="TOPGEN_4:th.5">Th5</a></i>;<br/>
<a NAME="E4:14"/><b>then </b>
 <a href="topgen_1.html#K4" title="TOPGEN_1:func.4">density</a> <font color="Maroon" title="c1">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="txt" href="topgen_4.html#E2:14"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:14"/>
<font color="Maroon" title="c1">T</font> is <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a>
 <b>by </b><i><a class="ref" href="card_1.html#T83" title="CARD_1:th.83">CARD_1:83</a>, <a class="ref" href="topgen_1.html#D13" title="TOPGEN_1:def.13">TOPGEN_1:def 13</a></i>;<br/>


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