Theorems · Theorem · general topology
Topology.IsOpenEmbedding.isEmbedding
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsOpenEmbedding f → Topology.IsEmbedding f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 22 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.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsOpenEmbedding.toIsEmbeddingproof · cited by 61
Cited by22
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.isOpenMapproof · cited by 50
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- Topology.IsOpenEmbedding.map_nhds_eqproof · cited by 22
- Topology.IsOpenEmbedding.isInducingproof · cited by 14
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- Topology.IsOpenEmbedding.measurableEmbeddingproof · cited by 5
- Topology.IsOpenEmbedding.isQuasiSeparated_iffproof · cited by 3
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2
- TopCat.pullback_map_isOpenEmbeddingproof · cited by 2
- Topology.IsConstructible.image_of_isOpenEmbeddingproof · cited by 2
- Topology.IsOpenEmbedding.quasiSoberproof · cited by 2
- Topology.IsOpenEmbedding.restrictproof · cited by 2