Theorems · Inductive type · general topology
PrespectralSpace
(X : Type u_3) → [TopologicalSpace X] → Prop
A space is prespectral if the lattice of compact opens forms a basis.
- Defined in
- Mathlib.Topology.Spectral.Prespectral
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by29
Results whose statement or proof uses this declaration.
- PrespectralSpace.isTopologicalBasisstatement and proof · cited by 7
- Function.locallyFinsupp.mapstatement and proof · cited by 4
- PrespectralSpace.of_isTopologicalBasisstatement · cited by 3
- Topology.IsLocallyConstructible.isConstructiblestatement and proof · cited by 2
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactstatement and proof · cited by 2
- Topology.IsLocallyConstructible.inter_of_isOpen_isCompactstatement and proof · cited by 1
- IsOpenMap.exists_opens_image_eq_of_prespectralSpacestatement and proof · cited by 1
- Function.locallyFinsupp.map_idstatement and proof · cited by 1
- PrespectralSpace.casesOnstatement and proof · cited by 1
- PrespectralSpace.exists_isCompact_and_isOpen_betweenstatement and proof · cited by 1
- PrespectralSpace.isBasis_opensstatement and proof · cited by 1
- PrespectralSpace.of_isInducingstatement and proof · cited by 1