Theorems · Theorem · general topology
Metric.isClosed_of_pairwise_le_dist
∀ {γ : Type w} [inst : MetricSpace γ] {s : Set γ} {ε : ℝ}, 0 < ε → (s.Pairwise fun x y => ε ≤ dist x y) → IsClosed s- Defined in
- Mathlib.Topology.MetricSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- IsClosedstatement · cited by 1,639
- Dist.diststatement and proof · cited by 1,539
- Set.Pairwisestatement and proof · cited by 321
- Metric.dist_mem_uniformityproof · cited by 23
- isClosed_of_spaced_outproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.