Theorems · Theorem · general topology
Metric.subsingleton_sphere
∀ {γ : Type w} [inst : MetricSpace γ] (x : γ) {r : ℝ}, r ≤ 0 → (Metric.sphere x r).Subsingleton- Defined in
- Mathlib.Topology.MetricSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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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
- MetricSpacestatement and proof · cited by 1,684
- Metric.spherestatement · cited by 371
- Set.Subsingletonstatement · cited by 276
- Metric.sphere_subset_closedBallproof · cited by 24
- Set.Subsingleton.antiproof · cited by 13
- Metric.subsingleton_closedBallproof · cited by 3
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