Theorems · Theorem · general topology

Filter.map_piMap_pi_finite

∀ {ι : Type u_1} {α : ι → Type u_4} {β : ι → Type u_5} [Finite ι] (f : (i : ι) → α i → β i)
  (l : (i : ι) → Filter (α i)), Filter.map (Pi.map f) (Filter.pi l) = Filter.pi fun i => Filter.map (f i) (l i)

Given finite families of maps f i : α i → β i and of filters l i : Filter (α i), the indexed product of f is maps the indexed product of the filters l i to the indexed products of their pushforwards under individual f is. See also map_piMap_pi for a more general case.

Defined in

Mathlib.Order.Filter.Cofinite

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Finite