Theorems · Theorem · field theory

Valued.integer.isDiscreteValuationRing_of_compactSpace

∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
  [hn : Valued.v.IsNontrivial] [CompactSpace ↥(Valued.integer K)], IsDiscreteValuationRing ↥(Valued.integer K)

Defined in: Mathlib.Topology.Algebra.Valued.LocallyCompact
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrderedCommGroupWithZero Valued Valuation.IsNontrivial CompactSpace

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Cites12

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

Fieldstatement and proof · cited by 7,404
Subringstatement · cited by 602
CompactSpacestatement and proof · cited by 593
LinearOrderedCommGroupWithZerostatement and proof · cited by 528
Valued.vstatement and proof · cited by 163
IsPrincipalIdealRingproof · cited by 131
IsDiscreteValuationRingstatement · cited by 117
Valuedstatement and proof · cited by 70
Valuation.IsNontrivialstatement and proof · cited by 27
Valued.integerstatement and proof · cited by 22
Valued.integer.isPrincipalIdealRing_of_compactSpaceproof · cited by 1
Valuation.isNontrivial_iff_not_a_fieldproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueFieldproof · cited by 0