Theorems · Theorem · general topology
lebesgue_number_lemma_of_emetric_sUnion
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} {c : Set (Set α)},
IsCompact s → (∀ t ∈ c, IsOpen t) → s ⊆ ⋃₀ c → ∃ δ > 0, ∀ x ∈ s, ∃ t ∈ c, Metric.eball x δ ⊆ t- Defined in
- Mathlib.Topology.EMetricSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites9
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
- IsOpenstatement and proof · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- Set.sUnionstatement and proof · cited by 392
- Metric.eballstatement and proof · cited by 294
- Set.sUnion_eq_iUnionproof · cited by 26
- lebesgue_number_lemma_of_emetricproof · cited by 1
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