Theorems · Theorem · functional analysis
Euclidean.nhds_basis_closedBall
∀ {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},
(nhds x).HasBasis (fun r => 0 < r) (Euclidean.closedBall x)- 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Filterproof · cited by 8,121
- nhdsstatement · cited by 5,554
- 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
- Filter.HasBasisstatement and proof · cited by 604
Cited by2
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3
- Euclidean.closedBall_mem_nhdsproof · cited by 0