Theorems · Inductive type · functional analysis
Seminorm
(𝕜 : Type u_12) → (E : Type u_13) → [SeminormedRing 𝕜] → [AddGroup E] → [SMul 𝕜 E] → Type u_13
A seminorm on a module over a normed ring is a function to the reals that is positive semidefinite, positive homogeneous, and subadditive.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 272 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- SeminormedRingAddGroupSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement · cited by 4,410
- SeminormedRingstatement · cited by 446
Cited by313
Results whose statement or proof uses this declaration.
- Seminorm.ballstatement and proof · cited by 78
- SeminormFamilyproof · cited by 68
- Seminorm.compstatement and proof · cited by 53
- Seminorm.closedBallstatement and proof · cited by 45
- normSeminormstatement · cited by 32
- Seminorm.extstatement and proof · cited by 17
- SchwartzMap.seminormstatement · cited by 16
- SeminormFamily.basisSets_iffstatement · cited by 16
- ContDiffMapSupportedIn.seminormstatement · cited by 15
- Seminorm.mem_ball_zerostatement and proof · cited by 11
- Seminorm.mem_ballstatement and proof · cited by 10
- Seminorm.toAddGroupSeminormstatement and proof · cited by 10
Showing the 200 most cited of 313.