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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b2">A</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="pscomp_1.html#V1" title="PSCOMP_1:attr.1">continuous</a>  <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b1">A</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">A</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> </span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c2">f</font> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a>, <a class="ref" href="topreal6.html#T83" title="TOPREAL6:th.83">TOPREAL6:83</a></span>;<br/>
<a NAME="E2:2"/>
 <a href="weierstr.html#K1" title="WEIERSTR:func.1">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">A</font></span>)</span> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="weierstr.html#T15" title="WEIERSTR:th.15">WEIERSTR:15</a>, <a class="ref" href="weierstr.html#T19" title="WEIERSTR:th.19">WEIERSTR:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/>
<font color="Maroon" title="c2">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">A</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="weierstr.html#D3" title="WEIERSTR:def.3">WEIERSTR:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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