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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel18.html#V2">injective</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of  <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="waybel18.html#K9">Sierpinski_Space</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="yellow_1.html#K3">BoolePoset</a> 1;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:74"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="waybel18.html#R1">is_Retract_of</a>  <a href="waybel18.html#K3">product</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span>
 <b>by </b><i><a class="ref" href="waybel18.html#T20">WAYBEL18:20</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>, <font color="Maroon">c<sub>7</sub></font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:74"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E2:74"><i><font color="Green">E42</font></i></a>, <a class="ref" href="waybel25.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being  <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of  <a href="yellow_1.html#K5">product</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span>;<br/>
<a NAME="E6:74"/><i><font color="Green">E44</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel18.html#T16">WAYBEL18:16</a></i>;<br/>
<a NAME="E7:74"/><i><font color="Green">E45</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel25.html#T3" target="_self">Th3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E9:74"/><i><font color="Green">E46</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>8</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>8</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 <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E10:74"/><i><font color="Green">E47</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel25.html#E9:74"><i><font color="Green">E46</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel25.html#E9:74"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel25.html#E10:74"><i><font color="Green">E47</font></i></a></i>;<br/>
<a NAME="E13:74"/><i><font color="Green">E48</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E10:74"><i><font color="Green">E47</font></i></a></i>;<br/>
<a NAME="E15:74"/><i><font color="Green">E49</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E9:74"><i><font color="Green">E46</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E9:74"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel25.html#E15:74"><i><font color="Green">E49</font></i></a></i>;<br/>
<a NAME="E18:74"/><i><font color="Green">E50</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel25.html#T16" target="_self">Th16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<a NAME="E20:74"/><i><font color="Green">E51</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</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>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
;<br/>
<a NAME="E21:74"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E6:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<a NAME="E22:74"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> #) <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>8</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>8</sub></font> #)
 
<b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E23:74"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E6:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel25.html#E10:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<a NAME="E24:74"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel25.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E25:74"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E9:74"><i><font color="Green">E46</font></i></a>, <a class="txt" href="waybel25.html#E15:74"><i><font color="Green">E49</font></i></a>, <a class="txt" href="waybel25.html#E18:74"><i><font color="Green">E50</font></i></a>, <a class="ref" href="waybel21.html#T6">WAYBEL21:6</a></i>;<br/>
<a NAME="E26:74"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>13</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="waybel17.html#T22">WAYBEL17:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a></i>;<br/>
<a NAME="E28:74"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</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>2</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> #)
 
;<br/>
<a NAME="E29:74"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>16</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E6:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel25.html#E26:74"><i><font color="Green">E53</font></i></a>, <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<a NAME="E30:74"/>
<font color="Maroon">c<sub>1</sub></font> <a href="waybel18.html#R1">is_Retract_of</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E2:74"><i><font color="Green">E42</font></i></a>, <a class="txt" href="waybel25.html#E6:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="txt" href="waybel25.html#E20:74"><i><font color="Green">E51</font></i></a>, <a class="ref" href="waybel25.html#T8" target="_self">Th8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="waybel25.html#V1" target="_self">monotone-convergence</a> <a href="pre_topc.html#NM1">TopSpace</a> <b>by </b><i><a class="ref" href="waybel25.html#T36" target="_self">Th36</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>12</sub></font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E10:74"><i><font color="Green">E47</font></i></a>, <a class="txt" href="waybel25.html#E13:74"><i><font color="Green">E48</font></i></a>, <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<a NAME="E33:74"/>
 <a href="waybel25.html#K1" target="_self">Omega</a> <span class="p1">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E6:74"><i><font color="Green">E44</font></i></a>, <a class="txt" href="waybel25.html#E7:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="waybel25.html#T13" target="_self">Th13</a></i>;<br/>
<b>then </b><i><font color="Green">E55</font></i>:  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <span class="p2">(<span class="default"><a href="waybel18.html#K3">product</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span></span>)</span></span>)</span> #) = 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K5">product</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> 1</span>)</span></span>)</span></span>)</span> #)
<b>by </b><i><a class="ref" href="waybel25.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>8</sub></font> #)
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>
;<br/>
<a NAME="E35:74"/>
<font color="Maroon">c<sub>14</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 
;<br/>
<a NAME="E36:74"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E15:74"><i><font color="Green">E49</font></i></a>, <a class="txt" href="waybel25.html#E34:74"><i><font color="Green">E55</font></i></a>, <a class="ref" href="waybel21.html#T6">WAYBEL21:6</a></i>;<br/>
<a NAME="E37:74"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="waybel17.html#T22">WAYBEL17:22</a></i>;<br/>
<a NAME="E38:74"/><b>then </b>
( <font color="Maroon">c<sub>16</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>14</sub></font> is <a href="pre_topc.html#V5">continuous</a> )
 
<b>by </b><i><a class="txt" href="waybel25.html#E21:74"><i><font color="Green">E52</font></i></a>, <a class="txt" href="waybel25.html#E29:74"><i><font color="Green">E54</font></i></a>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>hence </b><a NAME="E39:74"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</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>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)
 <b>by </b><i><a class="txt" href="waybel25.html#E4:74"><i><font color="Green">E43</font></i></a>, <a class="ref" href="yellow14.html#T34">YELLOW14:34</a></i>;<br/>


</div>
