Theorems · Theorem · general topology
Topology.WithLawson.isOpen_def
∀ {α : Type u_1} [inst : Preorder α] {T : Set (Topology.WithLawson α)},
IsOpen T ↔ TopologicalSpace.IsOpen (⇑Topology.WithLawson.toLawson ⁻¹' T)- Defined in
- Mathlib.Topology.Order.LawsonTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Set.preimagestatement · cited by 4,946
- IsOpenstatement · cited by 2,400
- TopologicalSpace.IsOpenstatement · cited by 25
- Topology.WithLawsonstatement and proof · cited by 12
- Topology.lawsonstatement · cited by 7
- Topology.WithLawson.toLawsonstatement · cited by 6
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