Theorems · Theorem · general topology
IsLocallyConstant.iff_continuous
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {x : TopologicalSpace Y} [DiscreteTopology Y] (f : X → Y),
IsLocallyConstant f ↔ Continuous f- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- DiscreteTopologystatement and proof · cited by 373
- IsLocallyConstantstatement · cited by 51
- Continuous.isOpen_preimageproof · cited by 51
- isOpen_discreteproof · cited by 36
- IsLocallyConstant.continuousproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Profinite.exists_homproof · cited by 1
- ProbabilityTheory.gaussian_charFunDual_congrproof · cited by 1
- DiscreteQuotient.proj_isLocallyConstantproof · cited by 1
- Profinite.Nobeling.isClosedEmbeddingproof · cited by 0