Theorems · Inductive type · commutative algebra
RingSeminorm
(R : Type u_2) → [NonUnitalNonAssocRing R] → Type u_2
A seminorm on a ring R is a function f : R → ℝ that preserves zero, takes nonnegative
values, is subadditive and submultiplicative and such that f (-x) = f x for all x ∈ R.
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonUnitalNonAssocRingstatement · cited by 354
Cited by87
Results whose statement or proof uses this declaration.
- RingSeminorm.toAddGroupSeminormstatement and proof · cited by 16
- smoothingFunstatement and proof · cited by 13
- seminormFromConst'statement and proof · cited by 13
- seminormFromConst_seqstatement and proof · cited by 13
- RingNorm.toRingSeminormstatement · cited by 11
- SeminormedRing.toRingSeminormstatement · cited by 10
- tendsto_seminormFromConst_seq_atTopstatement and proof · cited by 9
- tendsto_smoothingFun_of_map_one_le_onestatement and proof · cited by 7
- smoothingSeminormstatement and proof · cited by 5
- smoothingSeminormSeqstatement and proof · cited by 5
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5
- smoothingSeminormSeq_bddBelowstatement and proof · cited by 4