Theorems · Theorem · commutative algebra
seminormFromBounded_ker
∀ {R : Type u_1} [inst : CommRing R] {f : R → ℝ} {c : ℝ},
0 ≤ f → (∀ (x y : R), f (x * y) ≤ c * f x * f y) → seminormFromBounded' f ⁻¹' {0} = f ⁻¹' {0}If f : R → ℝ is a nonnegative, multiplicatively bounded function, then the kernel of
seminormFromBounded' f equals the kernel of f.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- seminormFromBounded'statement · cited by 17
- seminormFromBounded_eq_zero_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- seminormFromBounded_is_norm_iffproof · cited by 0