neg — Mathlib

English

Negation is realized as a continuous linear equivalence; it acts by the map x ↦ −x with continuous inverse x ↦ −x.

Русский

Отрицание реализовано как непрерывно-линейное эквивалентное отображение: x ↦ −x и обратное −x.

LaTeX

$$$\text{neg } : M \to M\;\text{is a continuous linear automorphism with } x \mapsto -x.$$$

Lean4

/-- The negation map as a continuous linear equivalence. -/
def neg [ContinuousNeg M] : M ≃L[R] M :=
  { LinearEquiv.neg R with
    continuous_toFun := continuous_neg
    continuous_invFun := continuous_neg }

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