Theorems · Theorem · functional analysis
convex_ball
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (a : E) (r : ℝ),
Convex ℝ (Metric.ball a r)- Defined in
- Mathlib.Analysis.Normed.Module.Convex
- Cited by
- 30 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.ballstatement · cited by 735
- Convexstatement and proof · cited by 551
- Set.sep_univproof · cited by 11
- ConvexOn.convex_ltproof · cited by 3
- convexOn_univ_distproof · cited by 2
Cited by30
Results whose statement or proof uses this declaration.
- hasFDerivAt_integral_of_dominated_of_fderiv_leproof · cited by 5
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- hasDerivAt_integral_of_dominated_loc_of_deriv_leproof · cited by 4
- IsOpen.isOpen_inter_preimage_of_fderiv_eq_zeroproof · cited by 3
- ConvexOn.continuousOn_tfaeproof · cited by 3
- uniformCauchySeqOn_ball_of_fderivproof · cited by 2
- Continuous.exists_contMDiff_approx_and_eqOnproof · cited by 2
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2
- ContDiffWithinAt.exists_lipschitzOnWithproof · cited by 2
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- HasFDerivWithinAt.curveIntegral_segment_source'proof · cited by 2