Theorems · Theorem · functional analysis
Euclidean.ball_eq_preimage
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E] [inst_2 : IsTopologicalAddGroup E]
[inst_3 : T2Space E] [inst_4 : Module ℝ E] [inst_5 : ContinuousSMul ℝ E] [inst_6 : FiniteDimensional ℝ E] (x : E)
(r : ℝ), Euclidean.ball x r = ⇑toEuclidean ⁻¹' Metric.ball (toEuclidean x) r- Cited by
- 2 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- ENNRealstatement · cited by 9,879
- Set.preimagestatement · cited by 4,946
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- IsTopologicalAddGroupstatement and proof · cited by 1,394
Cited by2
Results whose statement or proof uses this declaration.
- Euclidean.closure_ballproof · cited by 1
- Euclidean.exists_pos_lt_subset_ballproof · cited by 0