Theorems · Theorem · general topology
IsCompact.exists_thickening_subset_open
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s t : Set α},
IsCompact s → IsOpen t → s ⊆ t → ∃ δ, 0 < δ ∧ Metric.thickening δ s ⊆ t- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 156 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.
Cites10
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
- LE.le.transproof · cited by 3,151
- IsOpenstatement and proof · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsCompactstatement and proof · cited by 1,282
- Metric.thickeningstatement and proof · cited by 130
- Metric.cthickeningproof · cited by 113
- Metric.thickening_subset_cthickeningproof · cited by 12
- IsCompact.exists_cthickening_subset_openproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- Metric.hasBasis_nhdsSet_thickeningproof · cited by 2
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- IsCompact.exists_thickening_image_subsetproof · cited by 0