Editing Scott continuity (section)

==Examples==
The open sets in a given topological space when ordered by [[inclusion (set theory)|inclusion]] form a [[lattice (order)|lattice]] on which the Scott topology can be defined. A subset ''X'' of a topological space ''T'' is [[compact space|compact]] with respect to the topology on ''T'' (in the sense that every [[open cover]] of ''X'' contains a [[finite subcover]] of ''X'') if and only if the set of [[open neighbourhood]]s of ''X'' is open with respect to the Scott topology.<ref name="BauerTaylor2009">{{cite journal |author1=Bauer, Andrej  |author2=Taylor, Paul  |name-list-style=amp |year=2009 |title=The Dedekind Reals in Abstract Stone Duality |journal=Mathematical Structures in Computer Science |volume=19 |issue=4  |pages=757–838 |doi=10.1017/S0960129509007695 |url=http://PaulTaylor.EU/ASD/dedras/ |access-date=October 8, 2010 |citeseerx=10.1.1.424.6069  |s2cid=6774320 }}</ref>

{{anchor|curryApply}}For '''CPO''', the [[cartesian closed category]] of dcpo's, two particularly notable examples of Scott-continuous functions are [[currying|curry]] and [[apply]].<ref>{{cite book |last1=Barendregt |first1=H.P. |author-link1=Henk Barendregt |title=The Lambda Calculus |year=1984 |publisher=North-Holland |isbn=978-0-444-87508-2}} ''(See theorems 1.2.13, 1.2.14)''</ref>

[[Nuel Belnap]] used Scott continuity to extend [[logical connective]]s to a [[four-valued logic]].<ref>N.  Belnap (1975) "How Computers Should Think", pages 30 to 56 in ''Contemporary Aspects of Philosophy'', [[Gilbert Ryle]] editor, Oriel Press {{ISBN|0-85362-161-6}}</ref>