Theorems · Theorem · general topology
Filter.hasBasis_self
∀ {α : Type u_1} {l : Filter α} {P : Set α → Prop}, l.HasBasis (fun s => s ∈ l ∧ P s) id ↔ ∀ t ∈ l, ∃ r ∈ l, P r ∧ r ⊆ t- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Filter.HasBasisstatement · cited by 604
- Filter.mem_of_supersetproof · cited by 308
Cited by17
Results whose statement or proof uses this declaration.
- closed_nhds_basisproof · cited by 12
- uniformity_hasBasis_openproof · cited by 10
- nhds_basis_balancedproof · cited by 10
- IsCompact.nhdsSet_basis_isCompactproof · cited by 8
- compact_basis_nhdsproof · cited by 7
- UniformSpace.hasBasis_symmetricproof · cited by 5
- uniformity_hasBasis_closedproof · cited by 4
- locallyConnectedSpace_iff_connected_basisproof · cited by 2
- measurableSet_tendstoproof · cited by 2
- LocallyPathConnectedSpace.of_basesproof · cited by 2
- IsCompact.isCompact_isClosed_basis_nhdsproof · cited by 1
- locallyConvexSpace_iff_exists_convex_subset_zeroproof · cited by 1