Theorems · Definition · general topology
IsLocalMin
{α : Type u} → {β : Type v} → [TopologicalSpace α] → [Preorder β] → (α → β) → α → PropIsLocalMin f a means that f a ≤ f x for all x in some neighborhood of a.
- Defined in
- Mathlib.Topology.Order.LocalExtr
- Cited by
- 45 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
- IsMinFilterproof · cited by 36
Cited by45
Results whose statement or proof uses this declaration.
- IsLocalExtr.elimstatement · cited by 5
- IsLocalMin.hasDerivAt_eq_zerostatement and proof · cited by 4
- IsLocalMin.hasFDerivAt_eq_zerostatement and proof · cited by 4
- IsLocalMax.negstatement · cited by 3
- IsMinOn.isLocalMinstatement · cited by 3
- IsLocalMin.onstatement and proof · cited by 2
- IsLocalMinOn.isLocalMinstatement · cited by 2
- IsMinOn.of_isLocalMin_of_convex_univstatement and proof · cited by 1
- Polynomial.Chebyshev.isLocalMin_T_realstatement · cited by 1
- Complex.eventually_eq_or_eq_zero_of_isLocalMin_normstatement and proof · cited by 1
- isLocalMinOn_univ_iffstatement · cited by 1
- isLocalMin_of_deriv'statement · cited by 1