Theorems · Theorem · commutative algebra
isLinearTopology_iff_hasBasis_open_ideal
∀ {R : Type u_1} [inst : Ring R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R],
IsLinearTopology R R ↔ (nhds 0).HasBasis (fun I => IsOpen ↑I) fun I => ↑I- Defined in
- Mathlib.Topology.Algebra.LinearTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- nhdsstatement · cited by 5,554
- Idealstatement · cited by 4,748
- IsOpenstatement · cited by 2,400
- Filter.HasBasisstatement · cited by 604
- IsTopologicalRingstatement and proof · cited by 402
- IsLinearTopologystatement · cited by 83
- isLinearTopology_iff_hasBasis_open_submoduleproof · cited by 1
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