Theorems · Theorem · general topology
IsCompact.exists_cthickening_subset_open
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
IsCompact s → IsOpen t → s ⊆ t → ∃ δ, 0 < δ ∧ Metric.cthickening δ s ⊆ tIf s is compact, t is open and s ⊆ t, some cthickening of s is contained in t.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 155 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.
Cites14
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
- Compl.complproof · cited by 2,925
- IsOpenstatement and proof · cited by 2,400
- Disjointproof · cited by 2,201
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- Metric.cthickeningstatement and proof · cited by 113
- Disjoint.mono_rightproof · cited by 64
- IsOpen.isClosed_complproof · cited by 50
- Set.disjoint_compl_right_iff_subsetproof · cited by 10
- LE.le.disjoint_compl_rightproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- IsCompact.exists_thickening_subset_openproof · cited by 5
- Complex.exists_cthickening_tendstoUniformlyOnproof · cited by 2
- IsCompact.exists_isCompact_cthickeningproof · cited by 1
- Metric.hasBasis_nhdsSet_cthickeningproof · cited by 0