Theorems · Theorem · order theory
Topology.IsScott.isOpen_iff_scottContinuous_mem
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} [inst_1 : TopologicalSpace α] [Topology.IsScott α Set.univ],
IsOpen s ↔ ScottContinuous fun x => x ∈ s- Defined in
- Mathlib.Topology.Order.ScottTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Set.univstatement and proof · cited by 3,945
- IsOpenstatement and proof · cited by 2,400
- ScottContinuousstatement · cited by 24
- Topology.IsScottstatement and proof · cited by 20
- scottContinuousOn_univproof · cited by 3
- isOpen_iff_continuous_memproof · cited by 2
- Topology.IsScott.scottContinuousOn_iff_continuousproof · cited by 2
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