Mathlib Map

Theorems · Theorem · commutative algebra

Valued.isClopen_valuationSubring

∀ {Γ₀ : Type v} [inst : LinearOrderedCommGroupWithZero Γ₀] (K : Type u) [inst_1 : Field K] [hv : Valued K Γ₀],
  IsClopen ↑Valued.v.valuationSubring

The valuation subring of a valued field is clopen.

Defined in
Mathlib.Topology.Algebra.Valued.ValuationTopology
Cited by
0 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderedCommGroupWithZeroFieldValued

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.