Theorems · Theorem · general topology
continuous_of_le_add_edist
∀ {α : Type u_1} [inst : PseudoEMetricSpace α] {f : α → ENNReal} (C : ENNReal),
C ≠ ⊤ → (∀ (x y : α), f x ≤ f y + C * edist x y) → Continuous f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- LE.le.transproof · cited by 3,151
- Continuousstatement · cited by 2,592
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LT.lt.ne'proof · cited by 1,417
Cited by4
Results whose statement or proof uses this declaration.
- Metric.continuous_infEDistproof · cited by 9
- continuous_edistproof · cited by 9
- MeasureTheory.MeasuredSets.continuous_measureproof · cited by 1
- TopologicalSpace.Closeds.continuous_infEDistproof · cited by 1