Theorems · Theorem · general topology
IsMaxOn.isLocalMax
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β} {s : Set α} {a : α},
IsMaxOn f s a → s ∈ nhds a → IsLocalMax f a- Defined in
- Mathlib.Topology.Order.LocalExtr
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpacePreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- nhdsstatement and proof · cited by 5,554
- IsMaxOnstatement and proof · cited by 114
- IsLocalMaxstatement · cited by 50
- IsLocalMaxOn.isLocalMaxproof · cited by 2
- IsMaxOn.localizeproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Complex.isOpen_setOfPred_mem_nhds_and_isMaxOn_normproof · cited by 2
- isLocalMax_of_deriv_Iooproof · cited by 1
- isLocalMax_of_mono_antiproof · cited by 1
- IsCompact.exists_isLocalMax_mem_openproof · cited by 0