Theorems · Theorem · general topology
IsLocalHomeomorph.isOpenMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsLocalHomeomorph f → IsOpenMap fA local homeomorphism is an open map.
- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsOpenMapstatement · cited by 253
- ge_of_eqproof · cited by 67
- IsLocalHomeomorphstatement and proof · cited by 35
- IsOpenMap.of_nhds_leproof · cited by 10
- IsLocalHomeomorph.map_nhds_eqproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- IsCoveringMap.isOpenMapproof · cited by 3
- IsLocalDiffeomorph.isOpenMapproof · cited by 1
- IsLocalHomeomorph.isOpenEmbedding_of_injectiveproof · cited by 1
- IsLocalHomeomorph.toHomeomorphOfBijectiveproof · cited by 0
- Circle.isOpen_centeredArcproof · cited by 0