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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">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#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b2">A</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be  <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">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:()"><i><font color="Red">::  thesis: </font></i></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#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">A</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a></span><br/>





<b>reconsider </b><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>  <b>by </b><i><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></i>;<br/>
<a NAME="E2:1"/>
 <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#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 
<b>by </b><i><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></i>;<br/>
<b>hence </b><a NAME="E3:1"/>
<font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 <b>by </b><i><a class="ref" href="weierstr.html#D3" title="WEIERSTR:def.3">WEIERSTR:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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