Theorems · Inductive type · functional analysis
SeminormedAddCommGroup
Type u_8 → Type u_8
A seminormed group is an additive group endowed with a norm for which dist x y = ‖-x + y‖
defines a pseudometric space structure.
- Defined in
- Mathlib.Analysis.Normed.Group.Defs
- Cited by
- 2,671 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by3,073
Results whose statement or proof uses this declaration.
- NormedSpacestatement · cited by 12,499
- InnerProductSpacestatement · cited by 3,523
- NormedAddTorsorstatement · cited by 1,325
- LinearIsometryEquivstatement · cited by 748
- LinearIsometryEquiv.symmstatement and proof · cited by 287
- NormedAddGroupHomstatement · cited by 216
- LinearIsometrystatement · cited by 194
- dist_eq_normstatement · cited by 182
- MeasureTheory.DominatedFinMeasAdditivestatement and proof · cited by 138
- ContinuousLinearMap.flipstatement and proof · cited by 128
- LinearIsometryEquiv.toContinuousLinearEquivstatement and proof · cited by 125
- LinearMap.IsSymmetricstatement and proof · cited by 121
Showing the 200 most cited of 3,073.