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<span class="kw">let </span><font color="Maroon" title="c1">TM</font> be   <a href="pcomps_1.html#V3" title="PCOMPS_1:attr.3">metrizable</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <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"> ( <font color="Maroon" title="c1">TM</font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a>  iff <font color="Maroon" title="c1">TM</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a>  )</span><br/>

<div><span class="kw">hereby </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"> ( <font color="Maroon" title="c1">TM</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a>  implies <font color="Maroon" title="c1">TM</font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:45_1"/>
<font color="Maroon" title="c1">TM</font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a> 
 ; <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"> <font color="Maroon" title="c1">TM</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a> </span><br/><a NAME="E2:45_1"/><span class="kw">then </span>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">TM</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" onmouseover="rs('waybel23/D6')" onmouseout="rh()">WAYBEL23:def 6</a></span>;<br/><a NAME="E3:45_1"/><span class="kw">then </span>
 <a href="topgen_1.html#K4" title="TOPGEN_1:func.4">density</a> <font color="Maroon" title="c1">TM</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="metrizts.html#T22" target="_self" onmouseover="rs('metrizts/T22')" onmouseout="rh()">Th22</a></span>;<br/><span class="kw">hence </span><a NAME="E4:45_1"/>
<font color="Maroon" title="c1">TM</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" onmouseover="rs('topgen_1/D13')" onmouseout="rh()">TOPGEN_1:def 13</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/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:45"/>
<font color="Maroon" title="c1">TM</font> is  <a href="topgen_1.html#V7" title="TOPGEN_1:attr.7">separable</a> 
 ; <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"> <font color="Maroon" title="c1">TM</font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a> </span><br/>

<a NAME="E3:45"/><span class="kw">then </span>
 <a href="topgen_1.html#K4" title="TOPGEN_1:func.4">density</a> <font color="Maroon" title="c1">TM</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="topgen_1.html#D13" onmouseover="rs('topgen_1/D13')" onmouseout="rh()">TOPGEN_1:def 13</a></span>;<br/>
<a NAME="E4:45"/><span class="kw">then </span>
 <a href="waybel23.html#K2" title="WAYBEL23:func.2">weight</a> <font color="Maroon" title="c1">TM</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="metrizts.html#T22" target="_self" onmouseover="rs('metrizts/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<a NAME="E5:45"/><span class="kw">then </span>
<font color="Maroon" title="c1">TM</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>;<br/>
<span class="kw">hence </span><a NAME="E6:45"/>
<font color="Maroon" title="c1">TM</font> is  <a href="metrizts.html#V1" title="METRIZTS:attr.1">Lindelof</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="metrizts.html#E35"><span class="lab"><font color="Green" title="E28">Lm9</font></span></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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