Theorems · Definition · general topology
IsLocalMax
{α : Type u} → {β : Type v} → [TopologicalSpace α] → [Preorder β] → (α → β) → α → PropIsLocalMax f a means that f x ≤ f a for all x ∈ s in some neighborhood of a.
- Defined in
- Mathlib.Topology.Order.LocalExtr
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpacePreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- nhdsproof · cited by 5,554
- IsMaxFilterproof · cited by 38
Cited by50
Results whose statement or proof uses this declaration.
- IsLocalExtr.elimstatement · cited by 5
- IsMaxOn.isLocalMaxstatement · cited by 4
- IsLocalMax.negstatement and proof · cited by 3
- Complex.norm_eventually_eq_of_isLocalMaxstatement and proof · cited by 2
- MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 2
- DifferentiableAt.mem_interior_convex_of_surjective_fderivproof · cited by 2
- IsLocalMax.fderiv_eq_zerostatement and proof · cited by 2
- IsLocalMax.hasDerivAt_eq_zerostatement and proof · cited by 2
- IsLocalMax.hasFDerivAt_eq_zerostatement and proof · cited by 2
- IsLocalMaxOn.isLocalMaxstatement · cited by 2
- Complex.norm_eventually_eq_of_mdifferentiableAt_of_isLocalMaxstatement and proof · cited by 1
- isLocalMaxOn_univ_iffstatement · cited by 1