Theorems · Definition · general topology
oscillation
{E : Type u} → {F : Type v} → [PseudoEMetricSpace F] → [TopologicalSpace E] → (E → F) → E → ENNRealThe oscillation of f : E → F at x.
- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 5 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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- nhdsproof · cited by 5,554
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.mapproof · cited by 819
- Metric.ediamproof · cited by 159
Cited by5
Results whose statement or proof uses this declaration.
- oscillationWithin_univ_eq_oscillationstatement · cited by 2
- oscillationWithin_nhds_eq_oscillationstatement · cited by 1
- IsCompact.uniform_oscillationstatement and proof · cited by 0
- ContinuousAt.oscillation_eq_zerostatement · cited by 0
- Oscillation.eq_zero_iff_continuousAtstatement · cited by 0