Theorems · Definition · general topology
IsLocalExtr
{α : Type u} → {β : Type v} → [TopologicalSpace α] → [Preorder β] → (α → β) → α → PropIsLocalExtr f s a means IsLocalMin f s a ∨ IsLocalMax f s a.
- Defined in
- Mathlib.Topology.Order.LocalExtr
- Cited by
- 28 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
- IsExtrFilterproof · cited by 16
Cited by28
Results whose statement or proof uses this declaration.
- IsLocalExtr.elimstatement · cited by 5
- exists_isLocalExtr_Ioostatement and proof · cited by 3
- IsExtrOn.isLocalExtrstatement · cited by 3
- IsLocalExtr.hasDerivAt_eq_zerostatement and proof · cited by 3
- exists_hasDerivAt_eq_zero'proof · cited by 3
- IsLocalExtr.deriv_eq_zerostatement and proof · cited by 2
- IsLocalExtr.hasLineDerivAt_eq_zerostatement and proof · cited by 2
- IsLocalExtr.lineDeriv_eq_zerostatement and proof · cited by 2
- exists_deriv_eq_zeroproof · cited by 1
- exists_isLocalExtr_Ioo_of_tendstostatement and proof · cited by 1
- IsLocalExtrOn.isLocalExtrstatement · cited by 1
- Polynomial.Chebyshev.isLocalExtr_T_realstatement · cited by 1