Theorems · Theorem · general topology

LowerHemicontinuousAt.frequently

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

Alias of the forward direction of lowerHemicontinuousAt_iff_frequently.

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace