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Everything about Scott continuity
Definition of continuity for functions between posets
In mathematics, given two partially ordered sets P and Q, a function f: P → Q between them is Scott-continuous if it preserves all directed suprema. That is, for every directed subset D of P with supremum in P, its image has a supremum in Q, and that supremum is the image of the supremum of D, i.e. ∐f[D] = f(∐D), where ∐ is the directed join. When Q is the poset of truth values, i.e. Sierpiński space, then Scott-continuous functions are characteristic functions of open sets, and thus Sierpiński space is the classifying space for open sets. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Scott continuityA 5-minute orientation
- Pick up a classic book: Ascanius; Or, The Young Adventurer: Containing an Impartial History of the ...The most-reprinted book on the subject
- Read the landmark paper: Continuity of posets via Scott topology and sobrificationCited 29 times
- Go sideways: Complete partial orderA closely related topic
- Go sideways: Glossary of order theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Continuity of posets via Scott topology and sobrification
Robustness, Scott continuity, and computability
Continuity of Partially Ordered Soft Sets via Soft Scott Topology and Soft Sobrification
Scott Continuity in Generalized Probabilistic Theories
Giles Scott-Smith, ed. Obama, US Politics, and Transatlantic Relations. Change or Continuity , P. I.E. Peter Lang, 2012
📚 Books worth reading
Ascanius; Or, The Young Adventurer: Containing an Impartial History of the ...[author not identified] · 1841
A Biographical Dictionary of Eminent Scotsmen: With a Supplemental Volume ...Robert Chambers, Thomas Thomson · 1855
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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