Theorems · Theorem · functional analysis
BoundedContinuousFunction.norm_const_le
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : SeminormedAddCommGroup β] (b : β),
‖BoundedContinuousFunction.const α b‖ ≤ ‖b‖Norm of const α b is less than or equal to ‖b‖. If α is nonempty,
then it is equal to ‖b‖.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_rflproof · cited by 1,558
- norm_nonnegproof · cited by 725
- BoundedContinuousFunctionstatement · cited by 511
- BoundedContinuousFunction.conststatement · cited by 20
- BoundedContinuousFunction.norm_leproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.norm_const_eqproof · cited by 1
- BoundedContinuousFunction.nnnorm_const_leproof · cited by 0