Theorems · Definition · order theory

FiniteArchimedeanClass.ball

{M : Type u_1} →
  [inst : AddCommGroup M] →
    [inst_1 : LinearOrder M] →
      [inst_2 : IsOrderedAddMonoid M] →
        (K : Type u_2) →
          [inst_3 : Ring K] →
            [inst_4 : LinearOrder K] →
              [IsOrderedRing K] →
                [Archimedean K] → [inst_7 : Module K M] → [PosSMulMono K M] → FiniteArchimedeanClass M → Submodule K M

An open ball defined by ArchimedeanClass.submodule of UpperSet.Ioi c. For c = ⊤, we assign the junk value ⊥. This has the same carrier as ArchimedeanClass.ballAddSubgroup's.

Defined in

Mathlib.Algebra.Order.Module.Archimedean

Cited by

23 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidRingLinearOrderIsOrderedRingArchimedeanModulePosSMulMono