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<b>let </b><font color="Maroon" title="c2">C</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"> <span class="p1">(<span class="default"><a href="topreal1.html#K6" title="TOPREAL1:func.6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c2">C</font></span><br/>

<b>set </b><font color="Maroon" title="c3">A</font> = <span class="p1">(<span class="default"><a href="topreal1.html#K6" title="TOPREAL1:func.6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">A</font> = <span class="p1">(<span class="default"><a href="topreal1.html#K6" title="TOPREAL1:func.6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  non <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</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> <b>by </b><i><a class="ref" href="jordan2c.html#T130" title="JORDAN2C:th.130">JORDAN2C:130</a>, <a class="ref" href="topreal6.html#T99" title="TOPREAL6:th.99">TOPREAL6:99</a></i>;<br/>
<a NAME="E2:22"/>
<font color="Maroon" title="c4">A</font> is <a href="jordan1.html#V1" title="JORDAN1:attr.1">convex</a>
 
<b>by </b><i><a class="ref" href="jordan21.html#T6" title="JORDAN21:th.6">JORDAN21:6</a></i>;<br/>
<a NAME="E3:22"/><b>then </b>
<font color="Maroon" title="c4">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
;<br/>
<b>hence </b><a NAME="E4:22"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K6" title="TOPREAL1:func.6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1" title="JORDAN21:func.1">UMP</a> <font color="Maroon" title="c2">C</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="jordan.html#T10" target="_self" title="JORDAN:th.10">Th10</a>, <a class="ref" href="jordan2c.html#T133" title="JORDAN2C:th.133">JORDAN2C:133</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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