Theorems · Theorem · functional analysis
convex_eball
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (a : E) (r : ENNReal),
Convex ℝ (Metric.eball a r)- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- NNRealproof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- Convexstatement and proof · cited by 551
- Metric.eballstatement · cited by 294
- ENNReal.recTopCoeproof · cited by 48
- Metric.eball_coeproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Metric.isPathConnected_eballproof · cited by 1
- Metric.contractibleSpace_eballproof · cited by 1
- Metric.isPreconnected_eballproof · cited by 0