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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>;<br/>

<b>assume </b><a NAME="E1:69"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_6.html#K14" title="YELLOW_6:func.14">ConvergenceSpace</a> <span class="p1">(<span class="default"><a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">T</font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E2:69"/>
for <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">S</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> iff ( <font color="Olive" title="b1">S</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> &amp; <font color="Olive" title="b1">S</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) )
 <b>by </b><i><a class="ref" href="waybel11.html#T33" target="_self" title="WAYBEL11:th.33">Th33</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D4" target="_self" title="WAYBEL11:def.4">WAYBEL11:def 4</a><br/>


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