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<b>set </b><font color="Maroon">T</font> =  <a href="topgen_3.html#K2">Sorgenfrey-line</a> ;<br/>
<a NAME="E1:71"/><i><font color="Green">E42</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="topgen_3.html#K2">Sorgenfrey-line</a>  <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="topgen_3.html#D2">TOPGEN_3:def 2</a></i>;<br/>
<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">y</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>reconsider </b><font color="Maroon">A</font> =  <a href="limfunc1.html#K3">right_closed_halfline</a> <font color="Maroon">x</font>, <font color="Maroon">B</font> =  <a href="limfunc1.html#NK2" target="_self">left_open_halfline</a> <font color="Maroon">y</font> as  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topgen_3.html#K2">Sorgenfrey-line</a>  <b>by </b><i>, </i>;<br/>
<span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="limfunc1.html#NK2" target="_self">left_open_halfline</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K3">right_closed_halfline</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
<b>by </b><i><a class="ref" href="rcomp_3.html#T18">RCOMP_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="limfunc1.html#NK2" target="_self">left_open_halfline</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="limfunc1.html#K3">right_closed_halfline</a> <font color="Maroon">y</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="limfunc1.html#K3">right_closed_halfline</a> <font color="Maroon">y</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="borsuk_5.html#T99">BORSUK_5:99</a></i>
<br/>.= 
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="borsuk_5.html#T99">BORSUK_5:99</a></i>
;<br/>
<b>hence </b><a NAME="E4:71"/>
<span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="rcomp_2.html#K1">.[</a></span> is  <a href="pre_topc.html#V4">closed</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topgen_3.html#K2">Sorgenfrey-line</a> 
 <b>by </b><i><a class="ref" href="tops_1.html#T35">TOPS_1:35</a></i>;<br/>


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