Theorems · Theorem · functional analysis
ball_zero_eq
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (r : ℝ), Metric.ball 0 r = {x | ‖x‖ < r}- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.ofPredstatement · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- Set.extproof · cited by 2,266
- Metric.ballstatement · cited by 735
- SeminormedAddGroupstatement and proof · cited by 331
- dist_zero_rightproof · cited by 172
- Metric.mem_ballproof · cited by 47
Cited by8
Results whose statement or proof uses this declaration.
- HasFPowerSeriesWithinOnBall.uniform_geometric_approx'proof · cited by 3
- ContinuousLinearMap.opNorm_le_of_ballproof · cited by 3
- UpperHalfPlane.analyticAt_cuspFunction_zeroproof · cited by 2
- cauchySeq_finset_iff_vanishing_normproof · cited by 2
- HasFPowerSeriesWithinOnBall.uniform_geometric_approxproof · cited by 2
- SeminormFamily.basisSets_smul_rightproof · cited by 0
- ContinuousLinearMap.opNorm_le_of_shell'proof · cited by 0
- QuotientAddGroup.nhds_zero_hasBasisproof · cited by 0