seminormedCommGroup — Mathlib

English

If each G_i is a SeminormedCommGroup and ι is finite, then the product ∏_i G_i, endowed with the sup-norm, is a SeminormedCommGroup.

Русский

Если каждый G_i — полугруппа с нормой и ι конечен, то произведение ∏_i G_i с верхней нормой является SeminormedCommGroup.

LaTeX

$$Finite product of seminormed groups, using the sup norm on the product.$$

Lean4

/-- Finite product of seminormed groups, using the sup norm. -/
@[to_additive /-- Finite product of seminormed groups, using the sup norm. -/
    ]
instance seminormedCommGroup [∀ i, SeminormedCommGroup (G i)] : SeminormedCommGroup (∀ i, G i) :=
  { Pi.seminormedGroup with mul_comm := mul_comm }

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