Theorems · Theorem · general topology
Metric.frontier_closedBall_subset_sphere
∀ {α : Type u_2} [inst : PseudoMetricSpace α] {x : α} {ε : ℝ}, frontier (Metric.closedBall x ε) ⊆ Metric.sphere x ε- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- Metric.spherestatement · cited by 371
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- frontierstatement · cited by 214
- Continuous.distproof · cited by 20
- frontier_le_subset_eqproof · cited by 6
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