Theorems · Theorem · general topology
TopologicalSpace.vietoris.isClosedEmbedding_singleton
∀ {α : Type u_1} [inst : TopologicalSpace α] [T2Space α], Topology.IsClosedEmbedding fun x => {x}- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- T2Spacestatement and proof · cited by 1,351
- Topology.IsEmbeddingproof · cited by 294
- Topology.IsClosedEmbeddingstatement · cited by 195
- TopologicalSpace.vietorisstatement · cited by 34
- IsClopen.isOpenproof · cited by 21
- TopologicalSpace.vietoris.isOpen_inter_nonempty_of_isOpenproof · cited by 8
- TopologicalSpace.vietoris.isEmbedding_singletonproof · cited by 4
- TopologicalSpace.isClosed_range_singletonproof · cited by 2
- TopologicalSpace.vietoris.isClopen_singleton_emptyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isClosedEmbedding_singletonproof · cited by 1