Theorems · Theorem · functional analysis
Euclidean.isClosed_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}, IsClosed (Euclidean.closedBall x r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- IsClosedstatement · cited by 1,639
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- ContinuousSMulstatement and proof · cited by 1,016
- IsCompact.isClosedproof · cited by 77
- Euclidean.closedBallstatement · cited by 9
- Euclidean.isCompact_closedBallproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3