Theorems · Theorem · general topology
LocallyConstant.isLocallyConstant
∀ {X : Type u_5} {Y : Type u_6} [inst : TopologicalSpace X] (self : LocallyConstant X Y), IsLocallyConstant self.toFunThe map is locally constant.
- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 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.
- TopologicalSpacestatement and proof · cited by 24,529
- LocallyConstantstatement and proof · cited by 227
- IsLocallyConstantstatement · cited by 51
- LocallyConstant.toFunstatement · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- LocallyConstant.continuousproof · cited by 3
- Profinite.exists_locallyConstantproof · cited by 2
- Profinite.NobelingProof.factors_prod_eq_basis_of_eqproof · cited by 1
- Profinite.exists_locallyConstant_fin_twoproof · cited by 1
- LocallyConstant.apply_eq_of_preconnectedSpaceproof · cited by 1
- LocallyConstant.range_finiteproof · cited by 0
- LocallyConstant.apply_eq_of_isPreconnectedproof · cited by 0