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<b>let </b><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">SS</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">TS</font>,<font color="Maroon" title="c2">SS</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">TS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c2">SS</font> <a href="compts_1.html#NR2" title="COMPTS_1:NR.2">is_T2</a> 
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">SS</font>
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">PS</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>;<br/>

<b>assume </b><a NAME="E5:22"/>
<font color="Maroon" title="c4">PS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 ;<br/>

<a NAME="E6:22"/><b>then </b>
<font color="Maroon" title="c4">PS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 
<b>by </b><i><a class="txt" href="compts_1.html#E1:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="compts_1.html#T17" target="_self" title="COMPTS_1:th.17">Th17</a></i>;<br/>
<a NAME="E7:22"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">PS</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 
<b>by </b><i><a class="txt" href="compts_1.html#E3:22"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="compts_1.html#E4:22"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="compts_1.html#T24" target="_self" title="COMPTS_1:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c4">PS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="compts_1.html#E2:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="compts_1.html#T16" target="_self" title="COMPTS_1:th.16">Th16</a></i>;<br/>


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