Theorems · Theorem · general topology
oscillationWithin_univ_eq_oscillation
∀ {E : Type u} {F : Type v} [inst : PseudoEMetricSpace F] [inst_1 : TopologicalSpace E] (f : E → F) (x : E),
oscillationWithin f Set.univ x = oscillation f xThe oscillation of f at x within univ is equal to oscillation f x
- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 151 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.
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- Set.univstatement and proof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.univ_memproof · cited by 96
- oscillationWithinstatement · cited by 7
- oscillationstatement · cited by 5
- oscillationWithin_nhds_eq_oscillationproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Oscillation.eq_zero_iff_continuousAtproof · cited by 0
- ContinuousAt.oscillation_eq_zeroproof · cited by 0