Theorems · Theorem · general topology
Filter.tendstoCofinite_iff_finite_preimage_singleton
∀ {α : Type u_1} {β : Type u_2} (f : α → β), Filter.TendstoCofinite f ↔ ∀ (b : β), (f ⁻¹' {b}).Finite- Defined in
- Mathlib.Order.Filter.TendstoCofinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.preimagestatement and proof · cited by 4,946
- Set.Finitestatement and proof · cited by 1,814
- Filter.TendstoCofinitestatement and proof · cited by 28
- Filter.TendstoCofinite.finite_preimage_singletonproof · cited by 12
- Filter.Tendsto.cofinite_of_finite_preimage_singletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.tendstoCofinite_of_natDegree_ne_zeroproof · cited by 0