Theorems · Theorem · general topology
ContinuousAt.oscillation_eq_zero
∀ {E : Type u} {F : Type v} [inst : PseudoEMetricSpace F] [inst_1 : TopologicalSpace E] {f : E → F} {x : E},
ContinuousAt f x → oscillation f x = 0- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ContinuousAtstatement and proof · cited by 697
- continuousWithinAt_univproof · cited by 22
- oscillationstatement · cited by 5
- oscillationWithin_univ_eq_oscillationproof · cited by 2
- ContinuousWithinAt.oscillationWithin_eq_zeroproof · cited by 2
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