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<b>let </b><font color="Maroon" title="c1">S</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 <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">S</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a></span><br/>

<a NAME="E1:4"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c1">S</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T73" title="JORDAN2C:th.73">JORDAN2C:73</a></i>;<br/>
<a NAME="E2:4"/><b>then </b>
<a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">S</font> is <a href="rcomp_1.html#V2" title="RCOMP_1:attr.2">closed</a>
 
<b>by </b><i><a class="ref" href="jordan15.html#T3" target="_self" title="JORDAN15:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E3:4"/>
<a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">proj1</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">S</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 <b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="jordan1c.html#T4" title="JORDAN1C:th.4">JORDAN1C:4</a>, <a class="ref" href="rcomp_1.html#T29" title="RCOMP_1:th.29">RCOMP_1:29</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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