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<b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM2">SetSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<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> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:81"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">P</font> is <a href="jordan2c.html#V1">Bounded</a>
 <b>and </b><br/><a NAME="E2:81"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S</font> <a href="kurato_2.html#K7" target="_self">.</a> <font color="Olive">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 ;<br/>

<a NAME="E3:81"/><i><font color="Green">E54</font></i>: 
 <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">S</font> is <a href="pre_topc.html#V4">closed</a>
 
<b>by </b><i><a class="txt" href="kurato_2.html#E1:81"><i><font color="Green">E43</font></i></a></i>;<br/>
<a NAME="E4:81"/>
 <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">S</font> is <a href="jordan2c.html#V1">Bounded</a>
 
<b>by </b><i><a class="txt" href="kurato_2.html#E2:81"><i><font color="Green">E49</font></i></a>, <a class="ref" href="kurato_2.html#T4" target="_self">Th4</a>, </i>;<br/>
<b>hence </b><a NAME="E5:81"/>
 <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Maroon">S</font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i>, <a class="ref" href="topreal6.html#T88">TOPREAL6:88</a></i>;<br/>


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