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[Merged by Bors] - feat(Topology/ContinuousMap): add coeFnCLM #43746

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[Merged by Bors] - feat(Topology/ContinuousMap): add coeFnCLM #43746

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feat(Topology/ContinuousMap): add coeFnCLM
yuanyi-350 Sep 12, 2026
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yuanyi-350 Sep 16, 2026
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9 changes: 9 additions & 0 deletions Mathlib/Topology/ContinuousMap/Algebra.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -609,6 +609,15 @@ def coeFnLinearMap : C(α, M) →ₗ[R] α → M :=
{ (coeFnAddMonoidHom : C(α, M) →+ _) with
map_smul' := coe_smul }

/-- Coercion to a function as a `ContinuousLinearMap`. -/
@[simps! apply]
def coeFnCLM : C(α, M) →L[R] α → M where
__ := coeFnLinearMap R
cont := continuous_coeFun

@[simp]
lemma toLinearMap_coeFnCLM : (coeFnCLM R (α := α) (M := M)).toLinearMap = coeFnLinearMap R := rfl

variable (M) in
/-- Composition on the right by a continuous map, as a `ContinuousLinearMap`. -/
@[simps]
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