Theorems · Theorem · general topology
TopologicalSpace.vietoris.isEmbedding_singleton
∀ {α : Type u_1} [inst : TopologicalSpace α], Topology.IsEmbedding fun x => {x}- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 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.
Cites19
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
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- Set.image_congrproof · cited by 533
- Topology.IsEmbeddingstatement · cited by 294
- Set.image_imageproof · cited by 140
- Set.image_id'proof · cited by 86
- Set.powersetproof · cited by 67
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.isEmbedding_singletonproof · cited by 6
- TopologicalSpace.Compacts.isEmbedding_singletonproof · cited by 6
- TopologicalSpace.vietoris.isClosedEmbedding_singletonproof · cited by 1
- TopologicalSpace.vietoris.continuous_singletonproof · cited by 0