Theorems · Theorem · general topology
Metric.exists_ball_subset_ball
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε : ℝ},
y ∈ Metric.ball x ε → ∃ ε' > 0, Metric.ball y ε' ⊆ Metric.ball x ε- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- le_reflproof · cited by 2,061
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- Metric.ballstatement and proof · cited by 735
- sub_posproof · cited by 147
- sub_sub_selfproof · cited by 12
- Metric.ball_subsetproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Metric.isOpen_ballproof · cited by 63
- Complex.circleTransformDeriv_boundproof · cited by 0