Theorems · Theorem · functional analysis
BoundedContinuousFunction.norm_eq_iSup_norm
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : SeminormedAddCommGroup β]
(f : BoundedContinuousFunction α β), ‖f‖ = ⨆ x, ‖f x‖- Cited by
- 5 results in Mathlib
- Foundations
- Depth 123 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- iSupstatement and proof · cited by 2,415
- BoundedContinuousFunctionstatement and proof · cited by 511
- dist_zero_rightproof · cited by 172
- BoundedContinuousFunction.dist_eq_iSupproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousMap.norm_eq_iSup_normproof · cited by 4
- BoundedContinuousFunction.nnnorm_eq_iSup_nnnormproof · cited by 1
- ContDiffMapSupportedIn.seminorm_fderivLM_topproof · cited by 0
- ContDiffMapSupportedIn.seminorm_monoLM_eqproof · cited by 0
- ContDiffMapSupportedIn.norm_toBoundedContinuousFunctionproof · cited by 0