Theorems · Theorem · general topology
prespectralSpace_iff
∀ (X : Type u_3) [inst : TopologicalSpace X],
PrespectralSpace X ↔ TopologicalSpace.IsTopologicalBasis {U | IsOpen U ∧ IsCompact U}- Defined in
- Mathlib.Topology.Spectral.Prespectral
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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Cites8
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.ofPredstatement and proof · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- PrespectralSpacestatement and proof · cited by 23
- PrespectralSpace.casesOnproof · cited by 1
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