Theorems · Theorem · functional analysis
ball_normSeminorm
∀ (𝕜 : Type u_3) (E : Type u_7) [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E], (normSeminorm 𝕜 E).ball = Metric.ball
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Set.extproof · cited by 2,266
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballstatement · cited by 735
- dist_eq_normproof · cited by 182
- Seminorm.ballstatement · cited by 78
- normSeminormstatement and proof · cited by 32
Cited by7
Results whose statement or proof uses this declaration.
- NormedSpace.isVonNBounded_iffproof · cited by 9
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
- absorbent_ball_zeroproof · cited by 3
- gauge_unit_ballproof · cited by 1
- absorbent_ballproof · cited by 1
- balanced_ball_zeroproof · cited by 0
- InnerProductSpace.Core.topology_eqproof · cited by 0