continuousInv — Mathlib

English

In the product G × H, if G and H have continuous inverses, then the product has a continuous inverse given by (x,y)^{-1} = (x^{-1}, y^{-1}).

Русский

В произведении G × H инверсия действует по компонентам: (x,y)^{-1} = (x^{-1}, y^{-1}), и эта карта непрерывна при наличии непрерывных инверсий в G и H.

LaTeX

$$$\\\\operatorname{ContinuousInv}(G \\times H).$$$

Lean4

@[to_additive]
instance continuousInv [TopologicalSpace H] [Inv H] [ContinuousInv H] : ContinuousInv (G × H) :=
  ⟨continuous_inv.fst'.prodMk continuous_inv.snd'⟩

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