Theorems · Theorem · functional analysis
Euclidean.isCompact_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}
{r : ℝ}, IsCompact (Euclidean.closedBall x r)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 230 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
- Setproof · 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
- FiniteDimensionalstatement and proof · cited by 1,854
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousLinearEquiv.symmproof · cited by 368
Cited by2
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3
- Euclidean.isClosed_closedBallproof · cited by 1