Theorems · Theorem · functional analysis
ContinuousOn.norm
∀ {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
- 27 results in Mathlib
- Foundations
- Depth 158 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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement · cited by 5,413
- ContinuousOnstatement and proof · cited by 1,411
- SeminormedAddGroupstatement and proof · cited by 331
- ContinuousWithinAt.normproof · cited by 2
Cited by27
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- IsGreatest.norm_cfcproof · cited by 6
- IsGreatest.norm_cfcₙproof · cited by 5
- CFC.abs_eq_cfcₙ_coe_normproof · cited by 4
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
- Complex.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 2
- Real.tendstoLocallyUniformlyOn_rpow_sub_one_logproof · cited by 2
- ModularForm.multipliableLocallyUniformlyOn_one_sub_powproof · cited by 2
- TendstoUniformlyOn.tendsto_intervalIntegral_of_continuousOnproof · cited by 1
- CFC.abs_eq_cfc_normproof · cited by 1