Theorems · Theorem · commutative algebra
Valued.isClopen_integer
∀ (R : Type u) [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀],
IsClopen ↑Valued.v.integerThe closed unit ball of a valued ring is clopen.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsClopenstatement · cited by 189
- Valued.vstatement · cited by 163
- Valuedstatement and proof · cited by 70
- Valuation.integerstatement · cited by 68
- Valued.isOpen_integerproof · cited by 2
- Valued.isClosed_integerproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Valued.isClopen_valuationSubringproof · cited by 0