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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>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="pscomp_1.html#V9">continuous</a> <a href="pscomp_1.html#NM1">RealMap</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<a href="topmetr.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="topreal6.html#T83">TOPREAL6:83</a></i>;<br/>
<a NAME="E2:3"/>
<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="ref" href="weierstr.html#T15">WEIERSTR:15</a></i>;<br/>
<a NAME="E3:3"/><b>then </b>
 <a href="weierstr.html#K3">[#]</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span> is <a href="rcomp_1.html#V1">compact</a>
 
<b>by </b><i><a class="ref" href="weierstr.html#T19">WEIERSTR:19</a></i>;<br/>
<b>hence </b><a NAME="E4:3"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> is <a href="rcomp_1.html#V1">compact</a>
 <b>by </b><i><a class="ref" href="weierstr.html#D3">WEIERSTR:def 3</a></i>;<br/>


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