Theorems · Theorem · general topology
IsExtrFilter.comp_tendsto
∀ {α : Type u} {β : Type v} {δ : Type x} [inst : Preorder β] {f : α → β} {l : Filter α} {g : δ → α} {l' : Filter δ}
{b : δ}, IsExtrFilter f l (g b) → Filter.Tendsto g l' l → IsExtrFilter (f ∘ g) l' b- Defined in
- Mathlib.Order.Filter.Extr
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Tendstostatement and proof · cited by 3,814
- IsMaxFilterproof · cited by 38
- IsMinFilterproof · cited by 36
- IsExtrFilterstatement and proof · cited by 16
- IsMinFilter.isExtrproof · cited by 9
- IsMaxFilter.isExtrproof · cited by 8
- IsMaxFilter.comp_tendstoproof · cited by 4
- IsMinFilter.comp_tendstoproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsExtrFilter.hasLineDerivAt_eq_zeroproof · cited by 3
- IsLocalExtr.comp_continuousproof · cited by 0