Theorems · Theorem · general topology

ContinuousAt.finset_inf_apply

∀ {L : Type u_1} {X : Type u_2} [inst : TopologicalSpace L] [inst_1 : TopologicalSpace X] {ι : Type u_3}
  [inst_2 : SemilatticeInf L] [inst_3 : OrderTop L] [ContinuousInf L] {s : Finset ι} {f : ι → X → L} {x : X},
  (∀ i ∈ s, ContinuousAt (f i) x) → ContinuousAt (fun a => s.inf fun x => f x a) x

Defined in

Mathlib.Topology.Order.Lattice

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemilatticeInfOrderTopContinuousInf