Theorems · Theorem · general topology

LowerHemicontinuousWithinAt.comp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace γ]
  [inst_2 : TopologicalSpace β] {f : α → Set β} {s : Set α} {g : γ → α} {x : γ} {t : Set γ},
  LowerHemicontinuousWithinAt f s (g x) →
    ContinuousWithinAt g t x → Set.MapsTo g t s → LowerHemicontinuousWithinAt (f ∘ g) t x

Defined in

Mathlib.Topology.Semicontinuity.Defs

Cited by

1 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace