<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">Z</font> be  <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Y</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">Z</font><br/> for <font color="Olive" title="b2">f</font> being <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">Z</font>,<font color="Olive" title="b1">Y</font>  st <font color="Olive" title="b2">f</font> <a href="borsuk_1.html#NR1" title="BORSUK_1:NR.1">is_a_retraction</a>  holds <br/><font color="Olive" title="b1">Y</font> is <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a></span><br/><b>let </b><font color="Maroon" title="c2">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">Z</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">Z</font>,<font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b1">f</font> <a href="borsuk_1.html#NR1" title="BORSUK_1:NR.1">is_a_retraction</a>  holds <br/><font color="Maroon" title="c2">Y</font> is <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">Z</font>,<font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> <a href="borsuk_1.html#NR1" title="BORSUK_1:NR.1">is_a_retraction</a>  implies <font color="Maroon" title="c2">Y</font> is <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a> )</span><br/>





<b>assume </b><a NAME="E1:27"/>
<font color="Maroon" title="c3">f</font> <a href="borsuk_1.html#NR1" title="BORSUK_1:NR.1">is_a_retraction</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">Y</font> is <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a></span><br/>

<a NAME="E2:27"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="borsuk_1.html#R1" title="BORSUK_1:pred.1">is_a_retract_of</a> <font color="Maroon" title="c1">Z</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D20" title="BORSUK_1:def.20">BORSUK_1:def 20</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
<font color="Maroon" title="c2">Y</font> is <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a>
 <b>by </b><i><a class="ref" href="waybel25.html#T36" title="WAYBEL25:th.36">WAYBEL25:36</a>, <a class="ref" href="yellow16.html#T58" title="YELLOW16:th.58">YELLOW16:58</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
