Theorems · Theorem · functional analysis
mem_eball_one_iff
∀ {E : Type u_5} [inst : SeminormedGroup E] {a : E} {r : ENNReal}, a ∈ Metric.eball 1 r ↔ ‖a‖ₑ < r- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
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
- Metric.eballstatement · cited by 294
- SeminormedGroupstatement and proof · cited by 250
- Metric.mem_eballproof · cited by 18
- edist_one_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- mem_emetric_ball_one_iffproof · cited by 0