Theorems · Theorem · general topology

upperHemicontinuousAt_iff

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {x : α},
  UpperHemicontinuousAt f x ↔ ∀ t ∈ nhdsSet (f x), ∀ᶠ (x' : α) in nhds x, t ∈ nhdsSet (f x')

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace