Theorems · Theorem · functional analysis
Continuous.nnnorm
∀ {α : Type u_1} {E : Type u_4} [inst : SeminormedAddGroup E] [inst_1 : TopologicalSpace α] {f : α → E},
Continuous f → Continuous fun x => ‖f x‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 3 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement · cited by 4,310
- Continuousstatement · cited by 2,592
- NNNorm.nnnormstatement · cited by 952
- Continuous.compproof · cited by 371
- SeminormedAddGroupstatement and proof · cited by 331
- continuous_nnnormproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_innerproof · cited by 1
- CStarAlgebra.isClosed_nonnegproof · cited by 0