Theorems · Theorem · general topology

continuousOn_to_generateFrom_iff

∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} {β : Type u_5} {T : Set (Set β)} {f : α → β},
  ContinuousOn f s ↔ ∀ x ∈ s, ∀ t ∈ T, f x ∈ t → f ⁻¹' t ∈ nhdsWithin x s

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace