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<b>let </b><font color="Maroon" title="c1">T</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>; <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">S</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">T</font>  st <font color="Olive" title="b1">S</font> <a href="borsuk_1.html#R1" title="BORSUK_1:pred.1">is_a_retract_of</a> <font color="Maroon" title="c1">T</font> holds <br/><font color="Olive" title="b1">S</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font></span><br/><b>let </b><font color="Maroon" title="c2">S</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">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="borsuk_1.html#R1" title="BORSUK_1:pred.1">is_a_retract_of</a> <font color="Maroon" title="c1">T</font> implies <font color="Maroon" title="c2">S</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font> )</span><br/>



<b>given </b><font color="Maroon" title="c3">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">T</font>,<font color="Maroon" title="c2">S</font><b> such that </b><a NAME="E2:77"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="borsuk_1.html#NR1" title="BORSUK_1:NR.1">is_a_retraction</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_1.html#D20" title="BORSUK_1:def.20">BORSUK_1:def 20</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">S</font> <a href="waybel18.html#R1" title="WAYBEL18:pred.1">is_Retract_of</a> <font color="Maroon" title="c1">T</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">g</font> =  <a href="yellow_9.html#K1" title="YELLOW_9:func.1">incl</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">T</font> as  <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="c2">S</font>,<font color="Maroon" title="c1">T</font> <b>by </b><i><a class="ref" href="yellow16.html#T56" target="_self" title="YELLOW16:th.56">Th56</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">g</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D1" title="WAYBEL25:def.1">WAYBEL25:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> st <font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">S</font></span><br/>

<b>take </b>
<font color="Maroon" title="c3">f</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="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">S</font></span><br/>

<b>thus </b><a NAME="E4:77"/>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:77"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="yellow16.html#T57" target="_self" title="YELLOW16:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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