Theorems · Theorem · order theory
Topology.scottHausdorff_le_lower
∀ {α : Type u_1} [inst : Preorder α], Topology.scottHausdorff α Set.univ ≤ Topology.lower α- Defined in
- Mathlib.Topology.Order.ScottTopology
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 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.
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
- IsOpenproof · cited by 2,400
- Topology.scottHausdorffstatement and proof · cited by 10
- isLowerSet_univproof · cited by 8
- Topology.lowerstatement · cited by 7
- Topology.IsLower.isLowerSet_of_isOpenproof · cited by 4
- Topology.IsScottHausdorff.isOpen_of_isLowerSetproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Topology.scottHausdorff_le_lawsonproof · cited by 2
- Topology.IsLower.scottHausdorff_leproof · cited by 0