Theorems · Theorem · general topology

IsLocalMin.neg

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : AddCommGroup β] [inst_2 : PartialOrder β]
  [IsOrderedAddMonoid β] {f : α → β} {a : α}, IsLocalMin f a → IsLocalMax (fun x => -f x) a

Defined in

Mathlib.Topology.Order.LocalExtr

Cited by

1 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceAddCommGroupPartialOrderIsOrderedAddMonoid