Theorems · Theorem · general topology

ContinuousOn.sup

∀ {L : Type u_1} {X : Type u_2} [inst : TopologicalSpace L] [inst_1 : TopologicalSpace X] [inst_2 : Max L]
  [ContinuousSup L] {f g : X → L} {s : Set X}, ContinuousOn f s → ContinuousOn g s → ContinuousOn (fun a => f a ⊔ g a) s

Defined in

Mathlib.Topology.Order.Lattice

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceMaxContinuousSup