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<span class="kw">consider </span><font color="Maroon" title="c3">B</font> being   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E2:18_1_1"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="waybel23.html#T74" onmouseover="rs('waybel23/T74')" onmouseout="rh()">WAYBEL23:74</a></span>;<br/>
<a NAME="E3:18_1_1"/>
<font color="Maroon" title="c3">B</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">A</font> is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#T8" target="_self" onmouseover="rs('metrizts/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E4:18_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#T73" onmouseover="rs('waybel23/T73')" onmouseout="rh()">WAYBEL23:73</a></span>;<br/>
<a NAME="E5:18_1_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metrizts.html#T7" target="_self" onmouseover="rs('metrizts/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E6:18_1_1"/><span class="kw">then </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>  &amp;  <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <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="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="waybel23.html#D6" onmouseover="rs('waybel23/D6')" onmouseout="rh()">WAYBEL23:def 6</a></span>;<br/>
<a NAME="E7:18_1_1"/><span class="kw">then </span>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E8:18_1_1"/>
<font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">A</font> is  <a href="waybel23.html#V5" title="WAYBEL23:attr.5">second-countable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#D6" onmouseover="rs('waybel23/D6')" onmouseout="rh()">WAYBEL23:def 6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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