Theorems · Definition · general topology

UpperHemicontinuous

{α : Type u_1} → {β : Type u_2} → [TopologicalSpace α] → [TopologicalSpace β] → (α → Set β) → Prop

A function f : α → Set β is upper hemicontinuous if, for all x, whenever t is a neighborhood of f x, then t is a neighborhood of f x' for all x' sufficiently close to x.

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

30 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace