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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_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/>





<span class="kw">assume </span><a NAME="E1:26"/>
<font color="Maroon" title="c3">f</font> is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:26"/><span class="kw">then </span>
<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>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:26"/>
<font color="Maroon" title="c2">Y</font> is  <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#T36" onmouseover="rs('waybel25/T36')" onmouseout="rh()">WAYBEL25:36</a>, <a class="ref" href="yellow16.html#T56" onmouseover="rs('yellow16/T56')" onmouseout="rh()">YELLOW16:56</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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