Theorems · Theorem · general topology

ContinuousOn.finset_sup

∀ {L : Type u_1} {X : Type u_2} [inst : TopologicalSpace L] [inst_1 : TopologicalSpace X] {ι : Type u_3}
  [inst_2 : SemilatticeSup L] [inst_3 : OrderBot L] [ContinuousSup L] {s : Finset ι} {f : ι → X → L} {t : Set X},
  (∀ i ∈ s, ContinuousOn (f i) t) → ContinuousOn (s.sup f) t

Defined in

Mathlib.Topology.Order.Lattice

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceSemilatticeSupOrderBotContinuousSup