nhds_pi — Mathlib

English

In a quotient setting, the lift map Quotient.lift f hs is continuous when f is continuous and hs respects the quotient.

Русский

В условиях факторного пространства подъём Quotient.lift f hs непрерывен при условии непрерывности f и соответствия hs эквивалентности.

LaTeX

$$$$ \mathrm{Continuous}(\operatorname{Quotient.lift}(f, hs)) $$$$

Lean4

theorem nhds_pi {a : ∀ i, A i} : 𝓝 a = pi fun i => 𝓝 (a i) := by simp only [nhds_iInf, nhds_induced, Filter.pi]

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