Theorems · Theorem · general topology
Topology.IsClosedEmbedding.toIsEmbedding
∀ {X : Type u_1} {Y : Type u_2} [tX : TopologicalSpace X] [tY : TopologicalSpace Y] {f : X → Y},
Topology.IsClosedEmbedding f → Topology.IsEmbedding f- Defined in
- Mathlib.Topology.Defs.Induced
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Topology.IsEmbeddingstatement · cited by 294
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
Cited by27
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.isEmbeddingproof · cited by 25
- Topology.IsClosedEmbedding.isClosed_iff_image_isClosedproof · cited by 13
- Topology.IsClosedEmbedding.isProperMapproof · cited by 6
- Topology.IsClosedEmbedding.map_tsumproof · cited by 6
- Topology.IsEmbedding.sigmaMkproof · cited by 5
- ModelWithCorners.t1Spaceproof · cited by 5
- ContinuousMapZero.adjoin_id_denseproof · cited by 3
- QuasispectrumRestricts.cfcproof · cited by 2
- SpectrumRestricts.cfcproof · cited by 2
- Topology.IsClosedEmbedding.map_tprodproof · cited by 2
- Topology.IsClosedEmbedding.normalSpaceproof · cited by 2