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

<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:81"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c2">P</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 <b>and </b><br/><a NAME="E2:81"/><i><font color="Green" title="E50">A2</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">S</font> <a href="kurato_2.html#K7" title="KURATO_2:func.7">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 ;<br/>

<a NAME="E3:81"/><i><font color="Green" title="E51">A3</font></i>: 
 <a href="kurato_2.html#K8" title="KURATO_2:func.8">Lim_inf</a> <font color="Maroon" title="c1">S</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="ref" href="kurato_2.html#T52" target="_self" title="KURATO_2:th.52">Th52</a></i>;<br/>
<a NAME="E4:81"/>
 <a href="kurato_2.html#K8" title="KURATO_2:func.8">Lim_inf</a> <font color="Maroon" title="c1">S</font> is <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>
 
<b>by </b><i><a class="txt" href="kurato_2.html#E1:81"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="kurato_2.html#E2:81"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="kurato_2.html#T62" target="_self" title="KURATO_2:th.62">Th62</a></i>;<br/>
<b>hence </b><a NAME="E5:81"/>
 <a href="kurato_2.html#K8" title="KURATO_2:func.8">Lim_inf</a> <font color="Maroon" title="c1">S</font> is <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a>
 <b>by </b><i><a class="txt" href="kurato_2.html#E3:81"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="topreal6.html#T88" title="TOPREAL6:th.88">TOPREAL6:88</a></i>;<br/>


</div>
