Theorems · Theorem · commutative algebra
isLinearTopology_iff_hasBasis_open_twoSidedIdeal
∀ {R : Type u_1} [inst : Ring R] [inst_1 : TopologicalSpace R] [ContinuousAdd R],
IsLinearTopology R R ∧ IsLinearTopology Rᵐᵒᵖ 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 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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 and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- nhdsstatement and proof · cited by 5,554
- IsOpenstatement and proof · cited by 2,400
- MulOppositestatement and proof · cited by 1,135
- ContinuousAddstatement and proof · cited by 777
- Filter.HasBasisstatement and proof · cited by 604
- MulOpposite.unopproof · cited by 268
- TwoSidedIdealstatement and proof · cited by 151
- IsLinearTopologystatement and proof · cited by 83
- TwoSidedIdeal.mul_mem_leftproof · cited by 8
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