Theorems · Theorem · functional analysis
convex_closedBall
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (a : E) (r : ℝ),
Convex ℝ (Metric.closedBall a r)- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Metric.closedBallstatement · cited by 704
- Convexstatement and proof · cited by 551
- Set.sep_univproof · cited by 11
- ConvexOn.convex_leproof · cited by 3
- convexOn_univ_distproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- exists_mem_interior_convexHull_affineBasisproof · cited by 2
- convexHull_sphere_eq_closedBallproof · cited by 1
- sub_isBigO_norm_rpow_add_one_of_fderivproof · cited by 1
- Metric.isPreconnected_closedBallproof · cited by 1
- segment_subset_closedBall_leftproof · cited by 1
- StrictConvexSpace.of_norm_combo_ne_oneproof · cited by 1
- Metric.contractibleSpace_closedBallproof · cited by 0
- Metric.isPathConnected_closedBallproof · cited by 0
- StrictConvexSpace.of_norm_combo_lt_oneproof · cited by 0
- LinearMap.polar_AbsConvexproof · cited by 0