Theorems · Definition · general topology
Topology.lower
(α : Type u_1) → [Preorder α] → TopologicalSpace α
The lower topology is the topology generated by the complements of the left-closed right-infinite intervals.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- Compl.complproof · cited by 2,925
- Set.Iciproof · cited by 1,070
- TopologicalSpace.generateFromproof · cited by 62
Cited by10
Results whose statement or proof uses this declaration.
- Topology.lawsonproof · cited by 7
- Topology.IsLower.topology_eqstatement · cited by 5
- Topology.scottHausdorff_le_lowerstatement · cited by 2
- Topology.IsLower.topology_eq_lowerTopologystatement · cited by 2
- Topology.lawson_le_lowerstatement · cited by 1
- Topology.IsLower.casesOnstatement and proof · cited by 0
- Topology.IsLawson.isTopologicalBasisproof · cited by 0
- Topology.WithLower.isOpen_defstatement · cited by 0
- Topology.WithLower.isOpen_preimage_ofLowerstatement · cited by 0
- Topology.IsLower.recOnstatement and proof · cited by 0