Theorems · Theorem · general topology

IsLocalMaxOn.closure

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [inst_2 : Preorder Y]
  [OrderClosedTopology Y] {f : X → Y} {s : Set X} {a : X},
  IsLocalMaxOn f s a → ContinuousOn f (closure s) → IsLocalMaxOn f (closure s) a

Defined in

Mathlib.Topology.Order.ExtrClosure

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpacePreorderOrderClosedTopology