File: Mathlib/Topology/ContinuousFunction/LocallyConstant.lean

full_name: LocallyConstant.toContinuousMapMonoidHom_apply
code: /-- The inclusion of locally-constant functions into continuous functions as a multiplicative
monoid hom. -/
@[to_additive (attr := simps)
"The inclusion of locally-constant functions into continuous functions as an additive monoid hom."]
def toContinuousMapMonoidHom [Monoid Y] [ContinuousMul Y] : LocallyConstant X Y →* C(X, Y) 
goal: LocallyConstant.toContinuousMapMonoidHom f = ↑f

full_name: LocallyConstant.toContinuousMapAddMonoidHom
code: /-- The inclusion of locally-constant functions into continuous functions as a multiplicative
monoid hom. -/
@[to_additive (attr := simps)
"The inclusion of locally-constant functions into continuous functions as an additive monoid hom."]
def toContinuousMapMonoidHom [Monoid Y] [ContinuousMul Y] : LocallyConstant X Y →* C(X, Y) 
goal: LocallyConstant X Y →+ C(X, Y)

full_name: LocallyConstant.toContinuousMapMonoidHom
code: /-- The inclusion of locally-constant functions into continuous functions as a multiplicative
monoid hom. -/
@[to_additive (attr := simps)
"The inclusion of locally-constant functions into continuous functions as an additive monoid hom."]
def toContinuousMapMonoidHom [Monoid Y] [ContinuousMul Y] : LocallyConstant X Y →* C(X, Y) 
goal: LocallyConstant X Y →* C(X, Y)

full_name: LocallyConstant.toContinuousMapAddMonoidHom_apply
code: /-- The inclusion of locally-constant functions into continuous functions as a multiplicative
monoid hom. -/
@[to_additive (attr := simps)
"The inclusion of locally-constant functions into continuous functions as an additive monoid hom."]
def toContinuousMapMonoidHom [Monoid Y] [ContinuousMul Y] : LocallyConstant X Y →* C(X, Y) 
goal: LocallyConstant.toContinuousMapAddMonoidHom f = ↑f

full_name: LocallyConstant.toContinuousMapLinearMap_apply
code: /-- The inclusion of locally-constant functions into continuous functions as a linear map. -/
@[simps]
def toContinuousMapLinearMap (R : Type*) [Semiring R] [AddCommMonoid Y] [Module R Y]
    [ContinuousAdd Y] [ContinuousConstSMul R Y] : LocallyConstant X Y →ₗ[R] C(X, Y) 
goal: (LocallyConstant.toContinuousMapLinearMap R) f = ↑f

full_name: LocallyConstant.toContinuousMapLinearMap
code: /-- The inclusion of locally-constant functions into continuous functions as a linear map. -/
@[simps]
def toContinuousMapLinearMap (R : Type*) [Semiring R] [AddCommMonoid Y] [Module R Y]
    [ContinuousAdd Y] [ContinuousConstSMul R Y] : LocallyConstant X Y →ₗ[R] C(X, Y) 
goal: LocallyConstant X Y →ₗ[R] C(X, Y)

full_name: LocallyConstant.toContinuousMapAlgHom_apply
code: /-- The inclusion of locally-constant functions into continuous functions as an algebra map. -/
@[simps]
def toContinuousMapAlgHom (R : Type*) [CommSemiring R] [Semiring Y] [Algebra R Y]
    [TopologicalSemiring Y] : LocallyConstant X Y →ₐ[R] C(X, Y) 
goal: (LocallyConstant.toContinuousMapAlgHom R) f = ↑f

full_name: LocallyConstant.toContinuousMapAlgHom
code: /-- The inclusion of locally-constant functions into continuous functions as an algebra map. -/
@[simps]
def toContinuousMapAlgHom (R : Type*) [CommSemiring R] [Semiring Y] [Algebra R Y]
    [TopologicalSemiring Y] : LocallyConstant X Y →ₐ[R] C(X, Y) 
goal: LocallyConstant X Y →ₐ[R] C(X, Y)