Theorems · Theorem · general topology
Metric.isOpen_thickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] {δ : ℝ} {E : Set α}, IsOpen (Metric.thickening δ E)The (open) thickening is an open set.
- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 151 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
- IsOpenstatement · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealproof · cited by 863
- Metric.thickeningstatement · cited by 130
- Continuous.isOpen_preimageproof · cited by 51
- isOpen_Iioproof · cited by 38
- Metric.continuous_infEDistproof · cited by 9
- WithBot.LTproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- ae_eq_zero_of_integral_contMDiff_smul_eq_zeroproof · cited by 3
- tendsto_measure_thickeningproof · cited by 2
- IsClopen.of_thickening_subset_selfproof · cited by 2
- Metric.thickening_mem_nhdsSetproof · cited by 2
- MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasureproof · cited by 1
- MeasureTheory.levyProkhorovEDist_le_of_forall_leproof · cited by 1
- MeasureTheory.levyProkhorovEDist_triangleproof · cited by 1
- MeasureTheory.limsup_measure_closed_le_of_forall_tendsto_measureproof · cited by 1
- AddCircle.addWellApproximable_ae_empty_or_univproof · cited by 0
- IsCompact.exists_thickening_image_subsetproof · cited by 0
- Metric.thickening_subset_interior_cthickeningproof · cited by 0