Theorems · Theorem · general topology

IsLocalMaxOn.isLocalMax

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β} {s : Set α} {a : α},
  IsLocalMaxOn f s a → s ∈ nhds a → IsLocalMax f a

Defined in

Mathlib.Topology.Order.LocalExtr

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpacePreorder