Theorems · Definition · general topology
Topology.lawson
(α : Type u_2) → [Preorder α] → TopologicalSpace α
The Lawson topology is defined as the meet of Topology.lower and the Topology.scott.
- Defined in
- Mathlib.Topology.Order.LawsonTopology
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Set.univproof · cited by 3,945
- Topology.scottproof · cited by 9
- Topology.lowerproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- Topology.IsLawson.topology_eq_lawsonstatement · cited by 4
- Topology.lawson_le_scottstatement · cited by 2
- Topology.scottHausdorff_le_lawsonstatement · cited by 2
- Topology.lawson_le_lowerstatement · cited by 1
- Topology.WithLawson.isClosed_preimage_ofLawsonstatement · cited by 0
- Topology.WithLawson.isOpen_defstatement · cited by 0
- Topology.WithLawson.isOpen_preimage_ofLawsonstatement · cited by 0
- Topology.IsLawson.casesOnstatement and proof · cited by 0
- Topology.IsLawson.recOnstatement and proof · cited by 0