Theorems · Inductive type · general topology
Topology.IsLower
(α : Type u_3) → [t : TopologicalSpace α] → [Preorder α] → Prop
The lower topology is the topology generated by the complements of the left-closed right-infinite intervals.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpacePreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Preorderstatement · cited by 7,952
Cited by27
Results whose statement or proof uses this declaration.
- Topology.IsLower.topology_eqstatement and proof · cited by 5
- Topology.IsLower.isLowerSet_of_isOpenstatement and proof · cited by 4
- Topology.IsLower.isTopologicalBasisstatement and proof · cited by 3
- Topology.IsLower.continuous_iff_Icistatement and proof · cited by 2
- Topology.IsLower.isTopologicalBasis_insert_univ_subbasisstatement and proof · cited by 2
- Topology.IsLower.topology_eq_lowerTopologystatement and proof · cited by 2
- PrimitiveSpectrum.isClosed_iffstatement and proof · cited by 2
- sInfHom.continuousstatement and proof · cited by 1
- Topology.IsLower.closure_singletonstatement and proof · cited by 1
- Topology.IsLower.isClosed_upperClosurestatement and proof · cited by 1
- Topology.IsLower.isOpen_iff_generate_Ici_complstatement and proof · cited by 1
- Topology.IsLower.isTopologicalSpace_basisstatement and proof · cited by 1