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Theorems · Theorem · order theory

ScottContinuous.scottContinuousOn

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {D : Set (Set α)},
  ScottContinuous f → ScottContinuousOn D f
Defined in
Mathlib.Order.ScottContinuity
Cited by
4 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
PreorderPreorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ScottContinuous.fromProd · cited by 2ScottContinuous.fromProdScottContinuous.monotone · cited by 1ScottContinuous.monotoneScottContinuousOn.sup₂ · cited by 0ScottContinuousOn.sup₂ScottContinuous.ωScottContinuous · cited by 0ScottContinuous.ωScottCon…Set · cited by 53352SetPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptyIsLUB · cited by 280IsLUBDirectedOn · cited by 271DirectedOnScottContinuous · cited by 24ScottContinuousScottContinuousOn · cited by 18ScottContinuousOnScottContinuous.scottContinuo…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.