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<a NAME="E1:12_1_1"/>
 <a href="toprealb.html#K2" target="_self">IntIntervals</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> is <a href="tops_2.html#V1">open</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topalg_2.html#K3">R^1</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D1">TOPS_2:def 1</a><br/>

<b>assume </b><a NAME="E1:12_1_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="toprealb.html#K2" target="_self">IntIntervals</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:12_1_1_1"/><b>then </b>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  st <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">n</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
;<br/>
<b>hence </b><a NAME="E3:12_1_1_1"/>
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="jordan6.html#T46">JORDAN6:46</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:12_1_1"/>
 <a href="toprealb.html#K1" target="_self">IntIntervals</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> is  <a href="tops_2.html#V1">open</a> <a href="struct_0.html#NM3">Subset-Family</a> of <a href="topalg_2.html#K3">R^1</a> 
 ;<br/>


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