Theorems · Theorem · commutative algebra
IsAdic.isPrecomplete_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : UniformSpace R] [IsUniformAddGroup R] {I : Ideal R},
IsAdic I → (IsPrecomplete I R ↔ CompleteSpace R)IsPrecomplete I R is equivalent to being complete in the adic topology.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- Filterproof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- CompleteSpacestatement and proof · cited by 2,532
- Filter.atTopproof · cited by 2,405
- UniformSpacestatement and proof · cited by 2,040
- Filter.mapproof · cited by 819
- uniformityproof · cited by 765
Cited by2
Results whose statement or proof uses this declaration.
- IsPrecomplete.congr_ringEquivproof · cited by 0
- IsAdic.isAdicComplete_iffproof · cited by 0