Theorems · Theorem · general topology
Metric.finite_approx_of_totallyBounded
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α},
TotallyBounded s → ∀ ε > 0, ∃ t ⊆ s, t.Finite ∧ s ⊆ ⋃ y ∈ t, Metric.ball y ε- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 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.
Cites11
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
- Set.ofPredproof · cited by 6,101
- Set.iUnionstatement · cited by 2,483
- Set.Finitestatement · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- Metric.ballstatement · cited by 735
- TotallyBoundedstatement and proof · cited by 79
- Metric.dist_mem_uniformityproof · cited by 23
- totallyBounded_iff_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1