Theorems · Theorem · general topology
IsLocalHomeomorph.isOpenEmbedding_of_comp
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] {g : Y → Z} {f : X → Y},
IsLocalHomeomorph g → Topology.IsOpenEmbedding (g ∘ f) → Continuous f → Topology.IsOpenEmbedding fContinuous local sections of a local homeomorphism are open embeddings.
- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.injectiveproof · cited by 103
- Function.Injective.of_compproof · cited by 82
- Topology.IsOpenEmbedding.toIsEmbeddingproof · cited by 61
- IsLocalHomeomorphstatement and proof · cited by 35
- IsLocalHomeomorph.isOpenEmbedding_of_injectiveproof · cited by 1
- IsLocalHomeomorph.of_compproof · cited by 1
- Topology.IsOpenEmbedding.isLocalHomeomorphproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalHomeomorph.isTopologicalBasisproof · cited by 0