Theorems · Theorem · general topology

Filter.HasBasis.tendsto_iff

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} {ι' : Sort u_5} {la : Filter α} {pa : ι → Prop} {sa : ι → Set α}
  {lb : Filter β} {pb : ι' → Prop} {sb : ι' → Set β} {f : α → β},
  la.HasBasis pa sa →
    lb.HasBasis pb sb → (Filter.Tendsto f la lb ↔ ∀ (ib : ι'), pb ib → ∃ ia, pa ia ∧ ∀ x ∈ sa ia, f x ∈ sb ib)

Defined in

Mathlib.Order.Filter.Bases.Basic

Cited by

60 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Quot.sound