prodComm — Mathlib

English

The product of two spaces is canonically isomorphic to the swapped product.

Русский

Производство произведения пространств канонически изоморфно поменянному произведению.

LaTeX

$$$\\forall {\\alpha \\beta} [UniformSpace \\alpha] [UniformSpace \\beta],\\; ProdComm \\alpha \\beta : \\alpha \\times \\beta \\simeq_u \\beta \\times \\alpha$$$

Lean4

/-- `α × β` is uniformly isomorphic to `β × α`. -/
def prodComm : α × β ≃ᵤ β × α
    where
  uniformContinuous_toFun := uniformContinuous_snd.prodMk uniformContinuous_fst
  uniformContinuous_invFun := uniformContinuous_snd.prodMk uniformContinuous_fst
  toEquiv := Equiv.prodComm α β

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