Mathlib Map

Theorems · Theorem · general topology

Filter.atTop_countable_basis

∀ {α : Type u_1} [inst : Preorder α] [IsDirectedOrder α] [Nonempty α] [Countable α],
  Filter.atTop.HasCountableBasis (fun x => True) Set.Ici
Defined in
Mathlib.Order.Filter.AtTopBot.CountablyGenerated
Cited by
2 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderIsDirectedOrderNonemptyCountable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Measurable.liminf · cited by 2Measurable.liminfMeasurable.limsup · cited by 1Measurable.limsupPreorder · cited by 7952PreorderSet.ofPred · cited by 6101Set.ofPredFilter.atTop · cited by 2405Filter.atTopSet.Ici · cited by 1070Set.IciCountable · cited by 633CountableFilter.HasBasis · cited by 604Filter.HasBasisIsDirectedOrder · cited by 316IsDirectedOrderSet.to_countable · cited by 46Set.to_countableFilter.atTop_basis · cited by 42Filter.atTop_basisFilter.HasCountableBasis · cited by 9Filter.HasCountableBasisFilter.atTop_countable_basisCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.