Theorems · Theorem · general topology
Topology.IsClosedEmbedding.isEmbedding
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsClosedEmbedding f → Topology.IsEmbedding f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
Cited by25
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.continuousproof · cited by 25
- Topology.IsClosedEmbedding.isClosedMapproof · cited by 19
- Topology.IsClosedEmbedding.measurableEmbeddingproof · cited by 16
- Topology.IsClosedEmbedding.compproof · cited by 14
- Topology.IsClosedEmbedding.isInducingproof · cited by 10
- Topology.IsClosedEmbedding.tendsto_nhds_iffproof · cited by 4
- ModelWithCorners.map_nhds_eqproof · cited by 3
- Topology.IsClosedEmbedding.of_compproof · cited by 3
- Topology.IsClosedEmbedding.of_comp_iffproof · cited by 3
- HasCompactSupport.comp_isClosedEmbeddingproof · cited by 3
- QuasispectrumRestricts.cfcₙ_eq_restrictproof · cited by 2
- SpectrumRestricts.cfc_eq_restrictproof · cited by 2