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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> implies <font color="Maroon" title="c1">T</font> is <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a> )</span><br/>

<b>assume </b><a NAME="E1:7_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">T</font> is <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">T'</font> = <font color="Maroon" title="c1">T</font> as  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  ;<br/>
<a NAME="E3:7_1_1"/>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T'</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="topgen_2.html#D4" title="TOPGEN_2:def.4">TOPGEN_2:def 4</a></i>;<br/>
<a NAME="E4:7_1_1"/><b>then </b>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c2">T'</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
;<br/>
<b>hence </b><a NAME="E5:7_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a>
 <b>by </b><i><a class="ref" href="waybel23.html#D6" title="WAYBEL23:def.6">WAYBEL23:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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