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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1" target="_self">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="pre_topc.html#V2">correct</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E3:42_1_1"/><i><font color="Green">E29</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E5:42_1_1"/><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel19.html#E3:42_1_1"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="waybel_9.html#G1">TopRelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> #);<br/>
<a NAME="E7:42_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="waybel_9.html#G1">TopRelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> #),the <a href="orders_2.html#U1">InternalRel</a> of <a href="waybel_9.html#G1">TopRelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> #) #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="waybel_9.html#G1">TopRelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> #) as    <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E9:42_1_1"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>7</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>4</sub></font> #)
 
<b>by </b><i><a class="txt" href="waybel19.html#E3:42_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel19.html#E5:42_1_1"><i><font color="Green">E30</font></i></a></i>;<br/>
<a NAME="E10:42_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="pre_topc.html#V2">TopSpace-like</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T12">TEX_2:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> as    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>7</sub></font> <b>by </b><i><a class="txt" href="waybel19.html#E3:42_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel19.html#E5:42_1_1"><i><font color="Green">E30</font></i></a></i>;<br/>
<a NAME="E13:42_1_1"/>
 <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>8</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23">YELLOW_9:23</a></i>;<br/>
<a NAME="E14:42_1_1"/><b>then </b>
 <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>;<br/>
<a NAME="E15:42_1_1"/><b>then </b>
 <a href="cantor_1.html#K2">FinMeetCl</a> <font color="Maroon">c<sub>9</sub></font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="waybel19.html#E3:42_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel19.html#E5:42_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel19.html#E10:42_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>;<br/>
<a NAME="E16:42_1_1"/><b>then </b>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="waybel19.html#E10:42_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_9.html#T23">YELLOW_9:23</a></i>;<br/>
<a NAME="E17:42_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> is    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel19.html#E3:42_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel19.html#E5:42_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel19.html#E10:42_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>;<br/>
<b>hence </b><a NAME="E18:42_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> is <a href="waybel19.html#V2" target="_self">Lawson</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="waybel_9.html#V1">strict</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="pre_topc.html#V2">TopSpace-like</a> )
 <b>by </b><i><a class="ref" href="waybel19.html#T29" target="_self">Th29</a></i>;<br/>


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