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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 1</span>)</span>;<br/>



<b>assume </b><a NAME="E1:69"/>
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">q</font> where <font color="Olive">q</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 1</span>)</span> :  ex <font color="Olive">r</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Olive">r</font></span><a href="binarith.html#K11">*&gt;</a></span> &amp; <font color="Olive">r</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:69"/><b>then </b>
<font color="Maroon">P</font> is <a href="jordan1.html#V1">convex</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:69"/>
<font color="Maroon">P</font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="jordan1.html#T9">JORDAN1:9</a></i>;<br/>


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