Theorems · Definition · functional analysis
Euclidean.ball
{E : Type u_1} →
[inst : AddCommGroup E] →
[inst_1 : TopologicalSpace E] →
[IsTopologicalAddGroup E] →
[T2Space E] → [inst_4 : Module ℝ E] → [ContinuousSMul ℝ E] → [FiniteDimensional ℝ E] → E → ℝ → Set EOpen ball w.r.t. the Euclidean distance.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- FiniteDimensionalstatement and proof · cited by 1,854
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- ContinuousSMulstatement and proof · cited by 1,016
- Euclidean.distproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3
- Euclidean.ball_eq_preimagestatement · cited by 2
- Euclidean.ball_subset_closedBallstatement · cited by 1
- Euclidean.closure_ballstatement · cited by 1
- Euclidean.nhds_basis_ballstatement and proof · cited by 1
- Euclidean.ball_mem_nhdsstatement · cited by 0
- Euclidean.exists_pos_lt_subset_ballstatement and proof · cited by 0
- Euclidean.isOpen_ballstatement · cited by 0
- Euclidean.mem_ball_selfstatement · cited by 0