Theorems · Theorem · general topology

UpperHemicontinuous.inter

∀ {α : Type u_3} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β},
  UpperHemicontinuous f → ∀ {u : Set β}, IsClosed u → UpperHemicontinuous fun x => f x ∩ u

The pointwise intersection of an upper hemicontinuous function with a fixed closed set is upper hemicontinuous.

Defined in

Mathlib.Topology.Semicontinuity.Hemicontinuity

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace