Theorems · Theorem · general topology
PrespectralSpace.of_isTopologicalBasis
∀ {X : Type u_1} [inst : TopologicalSpace X] {B : Set (Set X)},
TopologicalSpace.IsTopologicalBasis B → (∀ U ∈ B, IsCompact U) → PrespectralSpace XA space is prespectral if it has a basis consisting of compact opens.
- Defined in
- Mathlib.Topology.Spectral.Prespectral
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.ofPredproof · cited by 6,101
- IsOpenproof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- TopologicalSpace.IsTopologicalBasis.isOpenproof · cited by 31
- PrespectralSpacestatement · cited by 23
- TopologicalSpace.IsTopologicalBasis.of_isOpen_of_subsetproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- PrespectralSpace.of_isInducingproof · cited by 1
- PrespectralSpace.of_isOpenCoverproof · cited by 0
- PrespectralSpace.of_isTopologicalBasis'proof · cited by 0