toLinearMapRingHom — Mathlib

English

For appropriate F and f, the kernel of f is a closed set in the domain, hence is a closed subspace.

Русский

Для соответствующих f множество ядерного ядра является замкнутым подпространством пространства домена.

LaTeX

$$$ \ker f \text{ is closed in } M_1 $$$

Lean4

/-- `ContinuousLinearMap.toLinearMap` as a `RingHom`. -/
@[simps]
def toLinearMapRingHom [ContinuousAdd M₁] : (M₁ →L[R₁] M₁) →+* M₁ →ₗ[R₁] M₁
    where
  toFun := toLinearMap
  map_zero' := rfl
  map_one' := rfl
  map_add' _ _ := rfl
  map_mul' _ _ := rfl

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