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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is  <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a>  implies <font color="Maroon" title="c1">T</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:14"/>
<font color="Maroon" title="c1">T</font> is  <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a> </span><br/>

<a NAME="E2:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#D6" title="WAYBEL23:def.6">WAYBEL23:def 6</a></span>;<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="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_4.html#T5" target="_self" title="TOPGEN_4:th.5">Th5</a></span>;<br/>
<a NAME="E4:14"/><span class="kw">then </span>
 <a href="topgen_1.html#K4" title="TOPGEN_1:func.4">density</a> <font color="Maroon" title="c1">T</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_1.html#D13" title="TOPGEN_1:def.13">TOPGEN_1:def 13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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