Theorems · Theorem · general topology
Topology.isOpenEmbedding_iff_continuous_injective_isOpenMap
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsOpenEmbedding f ↔ Continuous f ∧ Function.Injective f ∧ IsOpenMap f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Continuousstatement and proof · cited by 2,592
- IsOpenMapstatement and proof · cited by 253
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsOpenEmbedding.toIsEmbeddingproof · cited by 61
- Topology.IsOpenEmbedding.isOpenMapproof · cited by 50
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- Topology.IsOpenEmbedding.of_continuous_injective_isOpenMapproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.sumElimproof · cited by 0
- isLocalHomeomorphOn_iff_isOpenEmbedding_restrictproof · cited by 0