Theorems · Definition · general topology
IsMaxFilter
{α : Type u} → {β : Type v} → [Preorder β] → (α → β) → Filter α → α → Propis_maxFilter f l a means that f x ≤ f a for all x in some l-neighborhood of a
- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.Eventuallyproof · cited by 3,134
Cited by42
Results whose statement or proof uses this declaration.
- IsMaxOnproof · cited by 114
- IsLocalMaxproof · cited by 50
- IsLocalMaxOnproof · cited by 39
- IsExtrFilterproof · cited by 16
- IsMaxFilter.bicomp_monostatement and proof · cited by 8
- IsMaxFilter.isExtrstatement · cited by 8
- IsMaxFilter.filter_monostatement and proof · cited by 6
- IsExtrFilter.congrproof · cited by 5
- IsMaxFilter.comp_monostatement and proof · cited by 5
- IsExtrFilter.comp_monoproof · cited by 4
- IsExtrFilter.filter_monoproof · cited by 4
- IsMinFilter.comp_antitonestatement · cited by 4