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Theorems · Theorem · functional analysis

ContinuousAt.nnnorm

∀ {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
1 results in Mathlib
Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddGroupTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

eventually_nnnorm_sub_lt · cited by 1eventually_nnnorm_sub_ltTopologicalSpace · cited by 24529TopologicalSpaceNNReal · cited by 4310NNRealNNNorm.nnnorm · cited by 952NNNorm.nnnormContinuousAt · cited by 697ContinuousAtSeminormedAddGroup · cited by 331SeminormedAddGroupFilter.Tendsto.nnnorm · cited by 3Tendsto.nnnormContinuousAt.nnnormCITED BYCITES

Cites6

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Cited by1

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