Theorems · Theorem · general topology

lowerHemicontinuousWithinAt_singleton_iff

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {x : α}, LowerHemicontinuousWithinAt (fun x => {f x}) s x ↔ ContinuousWithinAt f s x

Defined in

Mathlib.Topology.Semicontinuity.Hemicontinuity

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace