Theorems · Definition · general topology
IsLocallyConstant
{X : Type u_1} → {Y : Type u_2} → [TopologicalSpace X] → (X → Y) → PropA function between topological spaces is locally constant if the preimage of any set is open.
- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.preimageproof · cited by 4,946
- IsOpenproof · cited by 2,400
Cited by56
Results whose statement or proof uses this declaration.
- LocallyConstant.isLocallyConstantstatement · cited by 7
- IsLocallyConstant.apply_eq_of_isPreconnectedstatement and proof · cited by 5
- IsLocallyConstant.tfaestatement and proof · cited by 5
- IsLocallyConstant.compstatement and proof · cited by 4
- IsLocallyConstant.comp₂statement and proof · cited by 4
- IsLocallyConstant.continuousstatement and proof · cited by 4
- IsLocallyConstant.iff_continuousstatement · cited by 4
- IsLocallyConstant.iff_exists_openstatement and proof · cited by 4
- IsLocallyConstant.iff_eventually_eqstatement and proof · cited by 3
- LocallyConstant.coe_mkstatement and proof · cited by 2
- IsLocallyConstant.apply_eq_of_preconnectedSpacestatement and proof · cited by 2
- IsLocallyConstant.conststatement · cited by 2