Theorems · Theorem · general topology

lowerHemicontinuousAt_iff

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {x : α},
  LowerHemicontinuousAt f x ↔ ∀ (u : Set β), IsOpen u → (f x ∩ u).Nonempty → ∀ᶠ (x' : α) in nhds x, (f x' ∩ u).Nonempty

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace