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<b>let </b><font color="Maroon">T</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <a href="numbers.html#K1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:92"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> is <a href="pscomp_1.html#V9" target="_self">continuous</a>
 ;<br/>

<b>assume </b><a NAME="E2:92"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">R</font> is <a href="pscomp_1.html#V3" target="_self">open</a>
 ;<br/>

<b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E3:92"/>
<font color="Maroon">P</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K1" target="_self">"</a> <font color="Maroon">f</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">R</font>
 ;<br/>

<b>then consider </b><font color="Maroon">eR</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:92"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">eR</font> <a href="hidden.html#R2">in</a>  <a href="pcomps_1.html#K1">bool</a> <a href="numbers.html#K1">REAL</a> 
 <b>and </b><br/><a NAME="E6:92"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">eR</font> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E7:92"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K1" target="_self">"</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">eR</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T115">FUNCT_2:115</a></i>;<br/>
<a NAME="E8:92"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">eR</font>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#D2" target="_self">Def2</a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">eR</font> = <font color="Maroon">eR</font> as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>by </b><i/>;<br/>
<a NAME="E10:92"/>
<font color="Maroon">eR</font> is <a href="rcomp_1.html#V3">open</a>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E11:92"/>
<font color="Maroon">P</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, , </i>;<br/>


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