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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>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="tops_1.html#V1">dense</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E40</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#D3">TOPS_1:def 3</a></i>;<br/>
<a NAME="E3:38"/><i><font color="Green">E47</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
 
<b>by </b><i>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>thus </b> <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span> = 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
<b>by </b><i>, <a class="ref" href="tops_2.html#T74">TOPS_2:74</a>, </i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
<b>by </b><i>, <a class="ref" href="funct_2.html#T45">FUNCT_2:45</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_1.html#D3">TOPS_1:def 3</a><br/>


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