Theorems · Theorem · functional analysis
balanced_ball_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
{r : ℝ}, Balanced 𝕜 (Metric.ball 0 r)Balls at the origin are balanced.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballstatement · cited by 735
- Balancedstatement and proof · cited by 77
- normSeminormproof · cited by 32
- ball_normSeminormproof · cited by 7
- Seminorm.balanced_ball_zeroproof · cited by 3
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