Theorems · Theorem · commutative algebra
IsAdic.isAdicComplete_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : UniformSpace R] [IsUniformAddGroup R] {I : Ideal R},
IsAdic I → (IsAdicComplete I R ↔ CompleteSpace R ∧ T2Space R)IsAdicComplete I R is equivalent to being complete and hausdorff in the adic topology.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- T2Spacestatement and proof · cited by 1,351
- IsUniformAddGroupstatement and proof · cited by 342
- IsAdicCompletestatement · cited by 124
- IsPrecompleteproof · cited by 29
- IsAdicstatement and proof · cited by 9
- IsAdic.isHausdorff_iffproof · cited by 2
- IsAdic.isPrecomplete_iffproof · cited by 2
- isAdicComplete_iffproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.