Theorems · Theorem · general topology
ContinuousOn.ofReal_map_toNNReal
∀ {f : NNReal → NNReal} {s : Set ℝ} {t : Set NNReal},
ContinuousOn f t → Set.MapsTo Real.toNNReal s t → ContinuousOn (fun x => ↑(f x.toNNReal)) s- Defined in
- Mathlib.Topology.Instances.NNReal.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- ContinuousOnstatement and proof · cited by 1,411
- NNReal.toRealstatement · cited by 1,260
- Set.MapsTostatement and proof · cited by 732
- Continuous.continuousOnproof · cited by 311
- Real.toNNRealstatement and proof · cited by 267
- continuous_subtype_valproof · cited by 159
- ContinuousOn.compproof · cited by 73
- Continuous.comp_continuousOnproof · cited by 52
- continuous_real_toNNRealproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- continuousOn_cfcₙ_nnrealproof · cited by 2
- continuousOn_cfc_nnrealproof · cited by 2
- cfc_nnreal_le_iffproof · cited by 0