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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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#K13" title="YELLOW_6:func.13">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> implies <font color="Maroon" title="c1">T</font> is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:68"/>
 <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#K13" title="YELLOW_6:func.13">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:68"/>
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>  ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#T33" target="_self" title="WAYBEL11:th.33">Th33</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel11.html#D4" target="_self" title="WAYBEL11:def.4">WAYBEL11:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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