Theorems · Theorem · functional analysis
ContinuousOn.nnnorm
∀ {α : Type u_1} {E : Type u_4} [inst : SeminormedAddGroup E] [inst_1 : TopologicalSpace α] {f : α → E} {s : Set α},
ContinuousOn f s → ContinuousOn (fun x => ‖f x‖₊) s- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NNRealstatement · cited by 4,310
- ContinuousOnstatement and proof · cited by 1,411
- NNNorm.nnnormstatement · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- ContinuousWithinAt.nnnormproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.