instIsTopologicalSemiring — Mathlib

English

The nonnegative real numbers form a topological semiring with the topology induced from \mathbb{R}; addition and multiplication are continuous.

Русский

Неотрицательные вещественные числа образуют топологическое полукольцо, операции сложения и умножения непрерывны в топологии, индуцированной от \mathbb{R}.

LaTeX

$$$\mathbb{R}_{\ge 0}$ with the usual topology is a topological semiring; the maps $(x,y) \mapsto x+y$ and $(x,y) \mapsto xy$ are continuous.$$

Lean4

instance : IsTopologicalSemiring ℝ≥0
    where
  toContinuousAdd := continuousAdd_induced toRealHom
  toContinuousMul := continuousMul_induced toRealHom

Похожие утверждения