Theorems · Theorem · general topology
lebesgue_number_lemma_of_emetric
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} {ι : Sort u_2} {c : ι → Set α},
IsCompact s → (∀ (i : ι), IsOpen (c i)) → s ⊆ ⋃ i, c i → ∃ δ > 0, ∀ x ∈ s, ∃ i, Metric.eball x δ ⊆ c i- Defined in
- Mathlib.Topology.EMetricSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- Set.iUnionstatement and proof · cited by 2,483
- IsOpenstatement and proof · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- Metric.eballstatement · cited by 294
- PseudoEMetricSpace.edist_commproof · cited by 52
- uniformity_basis_edistproof · cited by 17
- Filter.HasBasis.lebesgue_number_lemmaproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- lebesgue_number_lemma_of_emetric_sUnionproof · cited by 0