Theorems · Theorem · commutative algebra
Valued.isOpen_integer
∀ (R : Type u) [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀],
IsOpen ↑Valued.v.integerThe closed unit ball in a valued ring is open.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- one_ne_zeroproof · cited by 885
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valued.vstatement and proof · cited by 163
- Valuation.restrictproof · cited by 112
- Valuedstatement and proof · cited by 70
- Valuation.integerstatement · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- Valued.isClopen_integerproof · cited by 1
- Valued.isOpen_valuationSubringproof · cited by 0