Theorems · Theorem · general topology

lowerHemicontinuousWithinAt_iff_frequently

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {x : α}
  {s : Set α},
  LowerHemicontinuousWithinAt f s x ↔ ∀ (t : Set β), IsClosed t → (∃ᶠ (x' : α) in nhdsWithin x s, f x' ⊆ t) → f x ⊆ t

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

3 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace