Theorems · Definition · order theory
ArchimedeanClass.ballAddSubgroup
{M : Type u_1} →
[inst : AddCommGroup M] →
[inst_1 : LinearOrder M] → [inst_2 : IsOrderedAddMonoid M] → ArchimedeanClass M → AddSubgroup MAn open ball defined by ArchimedeanClass.addSubgroup of UpperSet.Ioi c.
For c = ⊤, we assign the junk value ⊥.
- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- AddSubgroupstatement · cited by 3,232
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement and proof · cited by 247
- UpperSet.Ioiproof · cited by 15
- ArchimedeanClass.addSubgroupproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ArchimedeanClass.ballAddSubgroup_antitonestatement · cited by 0
- ArchimedeanClass.ballAddSubgroup_topstatement and proof · cited by 0
- ArchimedeanClass.mem_ballAddSubgroup_iffstatement · cited by 0