Theorems · Theorem · general topology

IsLocalMinOn.comp_continuousOn

∀ {α : Type u} {β : Type v} {δ : Type x} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β}
  [inst_2 : TopologicalSpace δ] {t : Set α} {s : Set δ} {g : δ → α} {b : δ},
  IsLocalMinOn f t (g b) → s ⊆ g ⁻¹' t → ContinuousOn g s → b ∈ s → IsLocalMinOn (f ∘ g) s b

Defined in

Mathlib.Topology.Order.LocalExtr

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpacePreorderTopologicalSpace