Theorems · Theorem · general topology
Filter.HasAntitoneBasis.mem_iff
∀ {α : Type u_1} {ι : Type u_4} [inst : Preorder ι] {l : Filter α} {s : ι → Set α},
l.HasAntitoneBasis s → ∀ {t : Set α}, t ∈ l ↔ ∃ i, s i ⊆ t- Defined in
- Mathlib.Order.Filter.CountablyGenerated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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 and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.HasBasis.mem_iffproof · cited by 193
- Filter.HasAntitoneBasisstatement and proof · cited by 43
- Filter.HasAntitoneBasis.toHasBasisproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- exists_nhds_hasAntitoneBasis_absConvex_open_add_closure_subsetproof · cited by 0
- UniformSpace.completelyNormalSpace_of_hasAntitoneBasisproof · cited by 0