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<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D2">T_0TOPSP:def 2</a><br/>

<a NAME="E1:31_1_1"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">a</font> is   <a href="real_1.html#NM1">Real</a> &amp; <font color="Maroon">b</font> is   <a href="real_1.html#NM1">Real</a> )
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E2:31_1_1"/><i><font color="Green">E66</font></i>: 
(  <a href="topalg_2.html#K3">R^1</a>  <a href="hidden.html#R1">=</a> <a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="topalg_2.html#K3">R^1</a>  <a href="hidden.html#R1">=</a> <a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:31_1_1"/>
 <a href="toprealb.html#K6" target="_self">R^1</a> <span class="p1">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="tops_2.html#NR1" target="_self">is_homeomorphism</a> 
 
<b>by </b><i>, , <a class="ref" href="jordan16.html#T35">JORDAN16:35</a></i>;<br/>
<b>hence </b><a NAME="E4:31_1_1"/>
(  not <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a> or <span class="p1">(<span class="default"><a href="toprealb.html#K6" target="_self">R^1</a> <span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i>, <a class="ref" href="topgrp_1.html#T25">TOPGRP_1:25</a></i>;<br/>


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