Theorems · Theorem · functional analysis
ContinuousAt.norm
∀ {α : Type u_1} {E : Type u_4} [inst : SeminormedAddGroup E] [inst_1 : TopologicalSpace α] {f : α → E} {a : α},
ContinuousAt f a → ContinuousAt (fun x => ‖f x‖) a- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement · cited by 5,413
- ContinuousAtstatement and proof · cited by 697
- SeminormedAddGroupstatement and proof · cited by 331
- Filter.Tendsto.normproof · cited by 44
Cited by10
Results whose statement or proof uses this declaration.
- hasFDerivAt_norm_rpowproof · cited by 5
- ContDiffPointwiseHolderAt.comp_of_differentiableAtproof · cited by 3
- contDiff_norm_rpowproof · cited by 2
- Real.continuousAt_tanproof · cited by 2
- Complex.exp_sub_sum_range_isBigO_powproof · cited by 2
- Complex.continuousAt_tanproof · cited by 2
- eventually_norm_sub_ltproof · cited by 1
- circleAverage_re_herglotzRieszKernel_mul_log₀proof · cited by 1
- isPathConnected_sphereproof · cited by 1
- InnerProductGeometry.continuousAt_angleproof · cited by 1