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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<a NAME="E1:63"/>
(  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="waybel_3.html#V3">continuous</a> iff for <font color="Olive">b<sub>1</sub></font> being <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a> holds  <a href="waybel11.html#K5">sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> )
 
<b>by </b><i><a class="ref" href="waybel29.html#T34" target="_self">Th34</a></i>;<br/>
<b>hence </b><a NAME="E2:63"/>
(  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="waybel_3.html#V3">continuous</a> iff for <font color="Olive">b<sub>1</sub></font> being <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a> holds  <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1">Omega</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span> )
 <b>by </b><i><a class="ref" href="waybel29.html#T36" target="_self">Th36</a></i>;<br/>


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