Theorems · Theorem · general topology

UpperHemicontinuous.of_frequently

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

Alias of the reverse direction of upperHemicontinuous_iff_frequently.

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace