Theorems · Theorem · general topology
Filter.atTop_basis
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] [Nonempty α], Filter.atTop.HasBasis (fun x => True) Set.Ici- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement · cited by 2,405
- Set.Icistatement · cited by 1,070
- Filter.HasBasisstatement · cited by 604
- IsDirectedOrderstatement and proof · cited by 316
- Filter.HasAntitoneBasis.toHasBasisproof · cited by 26
- Filter.hasAntitoneBasis_atTopproof · cited by 2
Cited by42
Results whose statement or proof uses this declaration.
- Nat.cofinite_eq_atTopproof · cited by 37
- Filter.mem_atTop_setsproof · cited by 21
- Filter.frequently_atTopproof · cited by 14
- Filter.atBot_basisproof · cited by 14
- ENNReal.tendsto_atTop_zeroproof · cited by 11
- Metric.tendsto_atTopproof · cited by 10
- Filter.atTop_basis_Ioiproof · cited by 10
- HasSum.sigmaproof · cited by 8
- HasProd.sigmaproof · cited by 5
- Filter.HasBasis.cauchySeq_iffproof · cited by 5
- Metric.comap_dist_right_atTopproof · cited by 5
- Filter.limsup_eq_iInf_iSup_of_natproof · cited by 5