Theorems · Theorem · general topology

ContinuousOn.union_of_isOpen

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s t : Set α} {f : α → β},
  ContinuousOn f s → ContinuousOn f t → IsOpen s → IsOpen t → ContinuousOn f (s ∪ t)

If a function is continuous on two open sets, it is also continuous on their union.

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace