evalAlgHom — Mathlib

English

Under subsingleton α, Subalgebra(R, C(α,R)) is a singleton; all elements equal to algebraMap R C(α,R) (fdefault) etc.

Русский

При subsingleton α подпалгебра Subalgebra(R, C(α,R)) является одиночной; все элементы совпадают с algebraMap R C(α,R) (f по умолчанию).

LaTeX

$$$\\text{SubsingletonSubalgebra} : \\text{Subsingleton}(\\text{Subalgebra}(R, C(\\alpha,R))).$$$

Lean4

/-- Evaluation of continuous maps at a point, bundled as an algebra homomorphism. -/
@[simps]
def evalAlgHom (x : X) : C(X, R) →ₐ[S] R where
  toFun f := f x
  map_zero' := rfl
  map_one' := rfl
  map_add' _ _ := rfl
  map_mul' _ _ := rfl
  commutes' _ := rfl

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