Scott-open

adjective

Of a subset O of a partially ordered set P: such that it is an upper set and is inaccessible by directed joins, i.e. all directed sets D with supremum in O have non-empty intersection with O.

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Meanings

adjectiveScott-open (not comparable)
  1. not comparablemathematicsOf a subset O of a partially ordered set P: such that it is an upper set and is inaccessible by directed joins, i.e. all directed sets D with supremum in O have non-empty intersection with O.

Origin

Named after the mathematician Dana Scott.

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Cite this entry
APA

Scott-open. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Scott-open

MLA

“Scott-open.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Scott-open. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Scott-open,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Scott-open.

Source: Scott-open on Wiktionary, CC BY-SA 4.0.