Theorems · Theorem · general topology

Topology.IsQuotientMap.continuousOn_isOpen_iff

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] {f : α → β} {g : β → γ},
  Topology.IsQuotientMap f → ∀ {s : Set β}, IsOpen s → (ContinuousOn g s ↔ ContinuousOn (g ∘ f) (f ⁻¹' s))

Defined in

Mathlib.Topology.ContinuousOn

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace