Theorems · Definition · order theory
MulArchimedeanClass.ballSubgroup
{M : Type u_1} →
[inst : CommGroup M] → [inst_1 : LinearOrder M] → [inst_2 : IsOrderedMonoid M] → MulArchimedeanClass M → Subgroup MAn open ball defined by MulArchimedeanClass.subgroup 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.
- LinearOrderstatement and proof · cited by 8,572
- Subgroupstatement · cited by 3,593
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- MulArchimedeanClassstatement and proof · cited by 81
- UpperSet.Ioiproof · cited by 15
- MulArchimedeanClass.subgroupproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.mem_ballSubgroup_iffstatement · cited by 0
- MulArchimedeanClass.ballSubgroup_antitonestatement · cited by 0
- MulArchimedeanClass.ballSubgroup_topstatement and proof · cited by 0