Theorems · Theorem · field theory

Valued.integer.properSpace_iff_compactSpace_integer

∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
  [inst_3 : Valued.v.RankOne], ProperSpace K ↔ CompactSpace ↥(Valued.integer K)

Defined in: Mathlib.Topology.Algebra.Valued.LocallyCompact
Cited by: 0 results in Mathlib
Foundations: Depth 167 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
IsCompactproof · cited by 1,282
Metric.closedBallproof · cited by 704
Subringstatement · cited by 602
zero_lt_oneproof · cited by 598
CompactSpacestatement · cited by 593
LinearOrderedCommGroupWithZerostatement and proof · cited by 528
LocallyCompactSpaceproof · cited by 324
Set.image_univproof · cited by 322
ProperSpacestatement and proof · cited by 190
Subtype.range_coe_subtypeproof · cited by 170
Valued.vstatement and proof · cited by 163

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