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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">Z</font> be  <a href="waybel25.html#V1">monotone-convergence</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a>;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Z</font>;<br/>





<b>assume </b><a NAME="E1:32"/>
<font color="Maroon">Y</font> <a href="borsuk_1.html#R1">is_a_retract_of</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E2:32"/><b>then </b><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> <a href="yellow16.html#R3">is_a_retract_of</a>  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Z</font>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:32"/>
(  <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Z</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">Z</font> is <a href="waybel_3.html#V3">continuous</a> )
 ;<br/>

<a NAME="E4:32"/><b>then </b>
 <a href="waybel26.html#K1" target="_self">oContMaps</a> <font color="Maroon">X</font>,<font color="Maroon">Z</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/>
<b>hence </b><a NAME="E5:32"/>
(  <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> )
 <b>by </b><i>, <a class="ref" href="yellow16.html#T23">YELLOW16:23</a>, <a class="ref" href="yellow16.html#T24">YELLOW16:24</a></i>;<br/>


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