Theorems · Theorem · functional analysis
Seminorm.smul_ball_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{p : Seminorm 𝕜 E} {k : 𝕜} {r : ℝ}, k ≠ 0 → k • p.ball 0 r = p.ball 0 (‖k‖ * r)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement and proof · cited by 5,413
- Set.extproof · cited by 2,266
- mul_commproof · cited by 2,262
- Set.smulSetstatement · cited by 608
- NormedDivisionRingstatement and proof · cited by 360
- Seminormstatement and proof · cited by 272
- norm_pos_iffproof · cited by 168
Cited by5
Results whose statement or proof uses this declaration.
- NormedSpace.isVonNBounded_iffproof · cited by 9
- Seminorm.ball_zero_absorbs_ball_zeroproof · cited by 3
- WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedproof · cited by 2
- withSeminorms_iff_mem_nhds_isVonNBoundedproof · cited by 1
- with_gaugeSeminormFamilyproof · cited by 0