Theorems · Theorem · functional analysis
mem_eball_zero_iff
∀ {E : Type u_5} [inst : SeminormedAddGroup E] {a : E} {r : ENNReal}, a ∈ Metric.eball 0 r ↔ ‖a‖ₑ < r- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 148 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- ENorm.enormstatement and proof · cited by 715
- SeminormedAddGroupstatement and proof · cited by 331
- Metric.eballstatement · cited by 294
- edist_zero_rightproof · cited by 25
- Metric.mem_eballproof · cited by 18
Cited by8
Results whose statement or proof uses this declaration.
- HasFPowerSeriesWithinOnBall.uniform_geometric_approx'proof · cited by 3
- FormalMultilinearSeries.summable_norm_applyproof · cited by 3
- HasFPowerSeriesWithinOnBall.changeOriginproof · cited by 3
- HasFiniteFPowerSeriesOnBall.changeOriginproof · cited by 2
- HasFiniteFPowerSeriesOnBall.eq_partialSum'proof · cited by 2
- FormalMultilinearSeries.changeOrigin_evalproof · cited by 1
- HasFPowerSeriesOnBall.r_eq_top_of_existsproof · cited by 1
- mem_emetric_ball_zero_iffproof · cited by 0