Theorems · Theorem · general topology
ContinuousWithinAt.oscillationWithin_eq_zero
∀ {E : Type u} {F : Type v} [inst : PseudoEMetricSpace F] [inst_1 : TopologicalSpace E] {f : E → F} {D : Set E} {x : E},
ContinuousWithinAt f D x → oscillationWithin f D x = 0- Defined in
- Mathlib.Analysis.Oscillation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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 and proof · cited by 9,879
- LE.le.transproof · cited by 3,151
- zero_addproof · cited by 2,366
- nhdsWithinproof · cited by 1,912
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Filter.mapproof · cited by 819
- ne_of_gtproof · cited by 637
- ContinuousWithinAtstatement and proof · cited by 512
- Metric.eballproof · cited by 294
- Metric.ediamproof · cited by 159
Cited by2
Results whose statement or proof uses this declaration.
- OscillationWithin.eq_zero_iff_continuousWithinAtproof · cited by 1
- ContinuousAt.oscillation_eq_zeroproof · cited by 0