Theorems · Theorem · general topology
IsClosed.isLocallyClosed
∀ {X : Type u} {s : Set X} [inst : TopologicalSpace X], IsClosed s → IsLocallyClosed s- Defined in
- Mathlib.Topology.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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
- Set.univproof · cited by 3,945
- IsClosedstatement and proof · cited by 1,639
- Set.univ_interproof · cited by 258
- isOpen_univproof · cited by 112
- IsLocallyClosedstatement · cited by 44
Cited by12
Results whose statement or proof uses this declaration.
- jacobsonSpace_iff_locallyClosedproof · cited by 4
- Topology.IsClosedEmbedding.locallyCompactSpaceproof · cited by 3
- isLocallyClosed_Iciproof · cited by 2
- isLocallyClosed_tfaeproof · cited by 2
- isLocallyClosed_Iicproof · cited by 1
- TopologicalSpace.IsOpenCover.jacobsonSpace_iffproof · cited by 1
- Topology.IsOpenEmbedding.preimage_closedPointsproof · cited by 1
- LocallyCompactSpace.of_finiteDimensional_of_completeproof · cited by 1
- IsClosed.locallyCompactSpaceproof · cited by 1
- JacobsonSpace.of_isClosedEmbeddingproof · cited by 1
- isLocallyClosed_Iccproof · cited by 0