Scott continuity

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In mathematics, a monotone function

f : P → Q

between partially ordered sets P and Q is Scott-continuous if it preserves all directed suprema, i.e., if for every directed set D that has a supremum

sup D in P,

the set

{fx | x in D}

has the supremum

f(sup D) in Q.

This is in fact equivalent to being continuous with respect to the Scott topology on the respective posets.

See also: Glossary of order theory