Mathlib Map

Theorems · Definition · functional analysis

BoundedContinuousFunction.normComp

{α : Type u} →
  {β : Type v} →
    [inst : TopologicalSpace α] →
      [inst_1 : SeminormedAddCommGroup β] → BoundedContinuousFunction α β → BoundedContinuousFunction α ℝ

Taking the pointwise norm of a bounded continuous function with values in a SeminormedAddCommGroup yields a bounded continuous function with values in ℝ.

Defined in
Mathlib.Topology.ContinuousMap.Bounded.Normed
Cited by
3 results in Mathlib
Foundations
Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceSeminormedAddCommGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

BoundedContinuousFunction.norm_normComp · cited by 0BoundedContinuousFunction…BoundedContinuousFunction.coe_normComp · cited by 0BoundedContinuousFunction…BoundedContinuousFunction.bddAbove_range_norm_comp · cited by 0BoundedContinuousFunction…Real · cited by 25697RealTopologicalSpace · cited by 24529TopologicalSpaceNorm.norm · cited by 5413Norm.normSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupBoundedContinuousFunction · cited by 511BoundedContinuousFunctionBoundedContinuousFunction.comp · cited by 12BoundedContinuousFunction…BoundedContinuousFunction.nor…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.