Theorems · Theorem · general topology

ContinuousOn.div

∀ {α : Type u_1} {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : TopologicalSpace G₀] [ContinuousInv₀ G₀]
  [ContinuousMul G₀] {f g : α → G₀} [inst_4 : TopologicalSpace α] {s : Set α},
  ContinuousOn f s → ContinuousOn g s → (∀ x ∈ s, g x ≠ 0) → ContinuousOn (f / g) s

Defined in

Mathlib.Topology.Algebra.GroupWithZero

Cited by

11 results in Mathlib

Foundations

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

Assumes

GroupWithZeroTopologicalSpaceContinuousInv₀ContinuousMulTopologicalSpace