Theorems · Definition · general topology
LocallyConstant.toContinuousMap
{X : Type u_1} →
{Y : Type u_2} → [inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → LocallyConstant X Y → C(X, Y)We can turn a locally-constant function into a bundled ContinuousMap.
- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement · cited by 2,491
- LocallyConstantstatement and proof · cited by 227
- LocallyConstant.continuousproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- LocallyConstant.toContinuousMapAlgHomproof · cited by 3
- LocallyConstant.toContinuousMapLinearMapproof · cited by 3
- LocallyConstant.toContinuousMapAddMonoidHomproof · cited by 2
- CompHausLike.LocallyConstant.locallyConstantIsoContinuousMapproof · cited by 2
- LocallyConstant.toContinuousMapAlgHom_applystatement · cited by 1
- LocallyConstant.toContinuousMapMonoidHomproof · cited by 1
- LocallyConstant.toContinuousMapAddMonoidHom_applystatement · cited by 0
- LocallyConstant.toContinuousMapLinearMap_applystatement · cited by 0
- LocallyConstant.toContinuousMapMonoidHom_applystatement · cited by 0
- LocallyConstant.toContinuousMap_injectivestatement and proof · cited by 0
- CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_homstatement · cited by 0
- LocallyConstant.coe_continuousMapstatement · cited by 0