Theorems · Theorem · general topology
lebesgue_number_lemma_of_emetric_nhdsWithin
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α} {c : α → Set α},
IsCompact s → (∀ x ∈ s, c x ∈ nhdsWithin x s) → ∃ δ > 0, ∀ x ∈ s, ∃ y, Metric.eball x δ ∩ s ⊆ c y- Defined in
- Mathlib.Topology.EMetricSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites11
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- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsWithinstatement and proof · cited by 1,912
- 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_lemma_nhdsWithinproof · cited by 1
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