Theorems · Theorem · general topology
Metric.thickening_singleton
∀ {X : Type u} [inst : PseudoMetricSpace X] (δ : ℝ) (x : X), Metric.thickening δ {x} = Metric.ball x δ- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.extproof · cited by 2,266
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- Metric.ballstatement · cited by 735
- Metric.thickeningstatement · cited by 130
Cited by11
Results whose statement or proof uses this declaration.
- Metric.ball_subset_thickeningproof · cited by 4
- thickening_closedBallproof · cited by 3
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1
- thickening_ballproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- Metric.thickening_ballproof · cited by 0
- MeasureTheory.ProbabilityMeasure.continuous_piproof · cited by 0
- MeasureTheory.ProbabilityMeasure.continuous_prodproof · cited by 0
- cthickening_ballproof · cited by 0