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<a NAME="E1:48"/>
 <a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T4" title="YELLOW_1:th.4">YELLOW_1:4</a></span>;<br/>
<a NAME="E2:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow14.html#T1" title="YELLOW14:th.1">YELLOW14:1</a>, <a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c1">S</font> being   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> 1;<br/>
<a NAME="E4:48"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel18.html#T13" title="WAYBEL18:th.13">WAYBEL18:13</a></span>;<br/>
<a NAME="E5:48"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></span>;<br/>
<a NAME="E6:48"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel18.html#D9" title="WAYBEL18:def.9">WAYBEL18:def 9</a></span>;<br/>
<span class="kw">then </span> <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  = 
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">S</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="waybel25.html#T13" title="WAYBEL25:th.13">WAYBEL25:13</a></span>
<br/>.= 
<font color="Maroon" title="c1">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#T15" title="WAYBEL25:th.15">WAYBEL25:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:48"/>
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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