Theorems · Theorem · functional analysis
Euclidean.closure_ball
∀ {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}, r ≠ 0 → closure (Euclidean.ball x r) = Euclidean.closedBall x r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · 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.preimageproof · cited by 4,946
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- closurestatement and proof · cited by 1,254
Cited by1
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3