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<a NAME="E1:49"/>
 <a href="yellow_1.html#K3">BoolePoset</a> 1 <a href="hidden.html#R1">=</a>  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T4">YELLOW_1:4</a></i>;<br/>
<a NAME="E2:49"/><b>then </b><i><font color="Green">E36</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow14.html#T1">YELLOW14:1</a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<a NAME="E3:49"/><i><font color="Green">E38</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="waybel18.html#D9">WAYBEL18:def 9</a></i>;<br/>
<b>consider </b><font color="Maroon">S</font> being  <a href="waybel_9.html#V1">strict</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of  <a href="yellow_1.html#K3">BoolePoset</a> 1;<br/>
<a NAME="E5:49"/>
( the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="yellow_1.html#K3">BoolePoset</a> 1 )
 
<b>by </b><i><a class="ref" href="waybel18.html#T13">WAYBEL18:13</a>, <a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then </b> <a href="waybel25.html#K1">Omega</a> <a href="waybel18.html#K9">Sierpinski_Space</a>  = 
 <a href="waybel25.html#K1">Omega</a> <font color="Maroon">S</font>
<b>by </b><i><a class="ref" href="waybel27.html#D3" target="_self">Def3</a>, <a class="txt" href="waybel27.html#E2:49"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel25.html#T13">WAYBEL25:13</a></i>
<br/>.= 
<font color="Maroon">S</font>
<b>by </b><i><a class="ref" href="waybel25.html#T15">WAYBEL25:15</a></i>
;<br/>
<b>hence </b><a NAME="E7:49"/>
 <a href="waybel25.html#K1">Omega</a> <a href="waybel18.html#K9">Sierpinski_Space</a>  is <a href="waybel11.html#V4">Scott</a>
 ;<br/>


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