Theorems · Theorem · general topology
Metric.hasBasis_nhdsSet_thickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] {K : Set α},
IsCompact K → (nhdsSet K).HasBasis (fun δ => 0 < δ) fun δ => Metric.thickening δ K- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 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.
Cites12
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
- IsOpenproof · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- Filter.HasBasisstatement · cited by 604
- nhdsSetstatement · cited by 267
- Metric.thickeningstatement · cited by 130
- hasBasis_nhdsSetproof · cited by 20
- Filter.HasBasis.to_hasBasis'proof · cited by 14
- IsCompact.exists_thickening_subset_openproof · cited by 5
- Metric.thickening_mem_nhdsSetproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Metric.mem_nhdsSet_iffproof · cited by 0
- Metric.tendsto_nhdsSetproof · cited by 0