Theorems · Theorem · functional analysis
interior_closedBall
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] (x : E) {r : ℝ},
r ≠ 0 → interior (Metric.closedBall x r) = Metric.ball x r- Cited by
- 8 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- Set.preimageproof · cited by 4,946
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- Set.Iccproof · cited by 1,702
- Dist.distproof · cited by 1,539
- one_smulproof · cited by 1,374
Cited by8
Results whose statement or proof uses this declaration.
- frontier_closedBallproof · cited by 4
- combo_mem_ball_of_neproof · cited by 3
- interior_closedBall'proof · cited by 3
- centerMass_mem_ball_of_strictConvexSpaceproof · cited by 1
- EuclideanGeometry.Sphere.dist_center_lt_radius_of_sbtwproof · cited by 1
- ae_eq_const_or_norm_average_lt_of_norm_le_constproof · cited by 1
- StrictConvexSpace.of_norm_combo_ne_oneproof · cited by 1
- StrictConvexSpace.of_norm_combo_lt_oneproof · cited by 0