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<b>let </b><font color="Maroon">TS</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">SS</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">TS</font>,<font color="Maroon">SS</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">TS</font> is <a href="compts_1.html#V2" target="_self">compact</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">SS</font> <a href="compts_1.html#NR2" target="_self">is_T2</a> 
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green">E34</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">SS</font>
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">f</font> is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<b>let </b><font color="Maroon">PS</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">TS</font>;<br/>

<b>assume </b><a NAME="E5:22"/>
<font color="Maroon">PS</font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<a NAME="E6:22"/><b>then </b>
<font color="Maroon">PS</font> is <a href="compts_1.html#V6" target="_self">compact</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:22"/><b>then </b>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">PS</font> is <a href="compts_1.html#V6" target="_self">compact</a>
 
<b>by </b><i><a class="ref" href="compts_1.html#D1" target="_self">Def1</a>, <a class="ref" href="compts_1.html#D2" target="_self">Def2</a>, </i>;<br/>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">PS</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i>, </i>;<br/>


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