instBoundedSpaceProd — Mathlib

English

See 198524: the cobounded filter on a product equals the coproduct of the cobounded filters.

Русский

См. 198524: кобounded-фильтр произведения равен копродукту кобounded-фильтров.

LaTeX

$$$\\operatorname{cobounded}(\\forall i, X_i) = \\operatorname{Filter.coprod}ᵢ (\\lambda i, \\operatorname{cobounded}(X_i))$$$

Lean4

instance [BoundedSpace α] [BoundedSpace β] : BoundedSpace (α × β) := by simp [← cobounded_eq_bot_iff, cobounded_prod]

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