Theorems · Theorem · general topology
IsLocalHomeomorph.continuous
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsLocalHomeomorph f → Continuous fA local homeomorphism is continuous.
- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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
- Continuousstatement · cited by 2,592
- continuousOn_univproof · cited by 43
- IsLocalHomeomorphstatement and proof · cited by 35
- IsLocalHomeomorph.isLocalHomeomorphOnproof · cited by 6
- IsLocalHomeomorphOn.continuousOnproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalHomeomorph.isOpenEmbedding_of_injectiveproof · cited by 1
- IsLocalHomeomorph.toHomeomorphOfBijectiveproof · cited by 0