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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="realset2.html#V3">trivial</a> <a href="waybel25.html#V1">monotone-convergence</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E45</font></i>: 
(  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is <a href="lattice3.html#V3">complete</a> &amp;  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is <a href="waybel_3.html#V3">continuous</a> )
 ;<br/>

<a NAME="E2:38"/><b>then </b>
 <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="orders_2.html#NM1">Poset</a>
 
;<br/>
<a NAME="E3:38"/><b>then </b>
not <font color="Maroon">Y</font> <a href="urysohn1.html#NR1" target="_self">is_T1</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><b>then </b>
 <a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="waybel18.html#R1">is_Retract_of</a> <font color="Maroon">Y</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:38"/><b>then </b><i><font color="Green">E46</font></i>: 
(  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  is <a href="lattice3.html#V3">complete</a> &amp;  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  is <a href="waybel_3.html#V3">continuous</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:38"/>
 <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font>, <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:38"/><b>then </b>
 <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a> , <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="waybel_1.html#T7">WAYBEL_1:7</a></i>;<br/>
<b>hence </b><a NAME="E8:38"/>
 <a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font> is <a href="waybel_3.html#V3">continuous</a>
 <b>by </b><i>, <a class="ref" href="waybel15.html#T11">WAYBEL15:11</a></i>;<br/>


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