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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E42</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #)
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E43</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">Y</font> #)
 ;<br/>

<b>given </b><font color="Maroon">c</font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">X</font>, <font color="Maroon">r</font> being  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">S</font><b> such that </b><a NAME="E3:13"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">r</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c</font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D1" target="_self">WAYBEL25:def 1</a><br/>

<b>reconsider </b><font color="Maroon">cc</font> = <font color="Maroon">c</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">Y</font> <b>by </b><i>, , <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<b>reconsider </b><font color="Maroon">rr</font> = <font color="Maroon">r</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">Y</font>,<font color="Maroon">T</font> <b>by </b><i>, , <a class="ref" href="yellow12.html#T36">YELLOW12:36</a></i>;<br/>
<b>take </b>
<font color="Maroon">cc</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D1" target="_self">WAYBEL25:def 1</a><br/>

<b>take </b>
<font color="Maroon">rr</font>
;<br/>

<b>thus </b><a NAME="E6:13"/>
<font color="Maroon">rr</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">cc</font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font>
 <b>by </b><i>, </i>;<br/>


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