Theorems · Theorem · field theory

Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField

∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
  [Valued.v.RankOne],
  CompactSpace ↥(Valued.integer K) ↔
    CompleteSpace ↥(Valued.integer K) ∧ IsDiscreteValuationRing ↥(Valued.integer K) ∧ Finite (Valued.ResidueField K)

Defined in: Mathlib.Topology.Algebra.Valued.LocallyCompact
Cited by: 0 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrderedCommGroupWithZero Valued Valuation.RankOne

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Fieldstatement and proof · cited by 7,404
Set.univproof · cited by 3,945
Finitestatement and proof · cited by 3,029
CompleteSpacestatement and proof · cited by 2,532
Subringstatement · cited by 602
CompactSpacestatement and proof · cited by 593
LinearOrderedCommGroupWithZerostatement and proof · cited by 528
Valued.vstatement and proof · cited by 163
IsDiscreteValuationRingstatement and proof · cited by 117
Valuedstatement and proof · cited by 70
IsCompleteproof · cited by 68
Valuation.RankOnestatement and proof · cited by 32

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