Theorems · Theorem · general topology
Oscillation.eq_zero_iff_continuousAt
∀ {E : Type u} {F : Type v} [inst : PseudoEMetricSpace F] [inst_1 : TopologicalSpace E] (f : E → F) (x : E),
oscillation f x = 0 ↔ ContinuousAt f xThe oscillation of f at x is 0 if and only if f is continuous at x.
- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 9,879
- Set.univproof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ContinuousAtstatement and proof · cited by 697
- Set.mem_univproof · cited by 416
- continuousWithinAt_univproof · cited by 22
- oscillationWithinproof · cited by 7
- oscillationstatement · cited by 5
- oscillationWithin_univ_eq_oscillationproof · cited by 2
- OscillationWithin.eq_zero_iff_continuousWithinAtproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.