Theorems · Theorem · general topology

ContinuousAt.partialSups_apply

∀ {L : Type u_1} [inst : SemilatticeSup L] [inst_1 : TopologicalSpace L] [ContinuousSup L] {X : Type u_2}
  [inst_3 : TopologicalSpace X] {f : ℕ → X → L} {n : ℕ} {x : X},
  (∀ k ≤ n, ContinuousAt (f k) x) → ContinuousAt (fun a => (partialSups fun x => f x a) n) x

Defined in

Mathlib.Topology.Order.PartialSups

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupTopologicalSpaceContinuousSupTopologicalSpace