Theorems · Theorem · algebraic geometry
IsCompact.isRetrocompact
∀ {X : Type u_2} [inst : TopologicalSpace X] {U : Set X} [QuasiSeparatedSpace X],
IsCompact U → IsOpen U → IsRetrocompact U- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- QuasiSeparatedSpacestatement and proof · cited by 49
- IsRetrocompactstatement · cited by 43
- IsCompact.inter_of_isOpenproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactproof · cited by 2
- IsCompact.isConstructibleproof · cited by 2
- QuasiSeparatedSpace.isRetrocompact_iff_isCompactproof · cited by 1
- Topology.IsConstructible.induction_of_isTopologicalBasisproof · cited by 1