continuous_prod — Mathlib

English

For any α and n, the fixed-length vector space Vector α n carries a canonical topology.

Русский

Для любого типа α и длины n векторное пространство Vector α n имеет каноническую топологию.

LaTeX

$$$\\\\text{TopologicalSpace}(\\\\text{Vector}(\\\\alpha,n))$$$

Lean4

@[to_additive]
theorem continuous_prod [MulOneClass α] [ContinuousMul α] : Continuous (prod : List α → α) :=
  continuous_iff_continuousAt.mpr fun _l => tendsto_prod

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