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

<b>given </b><font color="Maroon">f</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">T</font>, <font color="Maroon">g</font> being  <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">S</font><b> such that </b><a NAME="E1:74"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</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">WAYBEL25:def 1</a><br/>

<b>given </b><font color="Maroon">h</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">R</font><b> such that </b><a NAME="E2:74"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">h</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D1">T_0TOPSP:def 1</a><br/>

<a NAME="E3:74"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">h</font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a> )
 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">R</font>,<font color="Maroon">T</font> <b>by </b><i><a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</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">R</font> <b>by </b><i><a class="txt" href="yellow16.html#E3:74"><i><font color="Green">E47</font></i></a>, <a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>;<br/>
<b>take </b>
<font color="Maroon">f'</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D1">WAYBEL25:def 1</a><br/>

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

<b>thus </b><a NAME="E6:74"/>
<font color="Maroon">g'</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f'</font> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">R</font>
 <b>by </b><i>, , </i>;<br/>


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