<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><a href="topreal1.html#K6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>;<br/>
<a NAME="E1:24"/>
not  <a href="topreal1.html#K6">north_halfline</a> <span class="p1">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T130">JORDAN2C:130</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="topreal1.html#K6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> as  non <a href="jordan2c.html#V1">Bounded</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="topreal6.html#T99">TOPREAL6:99</a></i>;<br/>
<a NAME="E3:24"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="jordan.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E4:24"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i><a class="ref" href="jordan21.html#T6">JORDAN21:6</a></i>;<br/>
<a NAME="E5:24"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan.html#E16"><i><font color="Green">Lemma12</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:24"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K6">north_halfline</a> <span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="jordan21.html#K1">UMP</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2">UBD</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="jordan.html#E3:24"><i><font color="Green">E14</font></i></a>, <a class="ref" href="jordan2c.html#T133">JORDAN2C:133</a></i>;<br/>


</div>
