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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">Y</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a> <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E29">A1</font></i>: 
(  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> &amp;  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> )
 ;<br/>

<a NAME="E2:38"/><b>then </b>
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>
 
;<br/>
<a NAME="E3:38"/><b>then </b>
 <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="ref" href="waybel26.html#T25" target="_self" title="WAYBEL26:th.25">Th25</a>, <a class="ref" href="waybel26.html#T26" target="_self" title="WAYBEL26:th.26">Th26</a></i>;<br/>
<a NAME="E4:38"/><b>then </b><i><font color="Green" title="E30">A2</font></i>: 
(  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> &amp;  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> )
 
<b>by </b><i><a class="txt" href="waybel26.html#E1:38"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="waybel26.html#T24" target="_self" title="WAYBEL26:th.24">Th24</a></i>;<br/>
<a NAME="E5:38"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a>  <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="waybel26.html#T6" target="_self" title="WAYBEL26:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>
 <b>by </b><i><a class="txt" href="waybel26.html#E4:38"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel15.html#T11" title="WAYBEL15:th.11">WAYBEL15:11</a>, <a class="ref" href="waybel_1.html#T7" title="WAYBEL_1:th.7">WAYBEL_1:7</a></i>;<br/>


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