Theorems · Theorem · general topology
Filter.TendstoCofinite.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
- 12 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.TendstoCofinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 4,946
- Set.Finitestatement · cited by 1,814
- Filter.TendstoCofinitestatement and proof · cited by 28
- Filter.TendstoCofinite.finite_preimageproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_renamestatement · cited by 7
- Filter.TendstoCofinite.mapDomainproof · cited by 4
- MvPowerSeries.coeff_embDomain_renameproof · cited by 3
- MvPowerSeries.rename_renameproof · cited by 3
- MvPowerSeries.rename_eq_substproof · cited by 2
- MvPowerSeries.rename_idproof · cited by 2
- MvPowerSeries.HasSubst.X_compproof · cited by 1
- MvPowerSeries.constantCoeff_renameproof · cited by 1
- Filter.tendstoCofinite_iff_finite_preimage_singletonproof · cited by 1
- Northcott.comp_of_finite_fibersproof · cited by 0
- Filter.TendstoCofinite.mapDomain_addproof · cited by 0
- MvPowerSeries.rename_mapproof · cited by 0