Theorems · Theorem · general topology
Metric.self_subset_thickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] {δ : ℝ}, 0 < δ → ∀ (E : Set α), E ⊆ Metric.thickening δ EA set is contained in its own (open) thickening.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 10 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.
Cites7
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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- subset_closureproof · cited by 309
- Metric.thickeningstatement · cited by 130
- Metric.closure_subset_thickeningproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- ae_eq_zero_of_integral_contMDiff_smul_eq_zeroproof · cited by 3
- infEDist_thickeningproof · cited by 3
- IsClopen.of_thickening_subset_selfproof · cited by 2
- Metric.thickening_mem_nhdsSetproof · cited by 2
- MeasureTheory.levyProkhorovEDist_selfproof · cited by 1
- MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasureproof · cited by 1
- Metric.thickening_eq_empty_iff_of_posproof · cited by 1
- MeasureTheory.limsup_measure_closed_le_of_forall_tendsto_measureproof · cited by 1
- Metric.diam_thickening_leproof · cited by 0
- IsCompact.exists_thickening_image_subsetproof · cited by 0