Theorems · Definition · general topology
oscillationWithin
{E : Type u} → {F : Type v} → [PseudoEMetricSpace F] → [TopologicalSpace E] → (E → F) → Set E → E → ENNRealThe oscillation of f : E → F within D at x.
- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- nhdsWithinproof · cited by 1,912
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.mapproof · cited by 819
- Metric.ediamproof · cited by 159
Cited by7
Results whose statement or proof uses this declaration.
- oscillationWithin_univ_eq_oscillationstatement · cited by 2
- IsCompact.uniform_oscillationWithinstatement and proof · cited by 2
- ContinuousWithinAt.oscillationWithin_eq_zerostatement and proof · cited by 2
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- OscillationWithin.eq_zero_iff_continuousWithinAtstatement and proof · cited by 1
- oscillationWithin_nhds_eq_oscillationstatement and proof · cited by 1
- Oscillation.eq_zero_iff_continuousAtproof · cited by 0