Theorems · Theorem · general topology
Metric.isPreconnected_closedBall
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [NormedSpace ℝ E] {x : E} {r : ℝ}, IsPreconnected (Metric.closedBall x r)- Defined in
- Mathlib.Analysis.Normed.Module.Connected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Metric.closedBallstatement · cited by 704
- IsPreconnectedstatement · cited by 205
- Convex.isPreconnectedproof · cited by 14
- convex_closedBallproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Metric.isConnected_closedBallproof · cited by 1