Theorems · Theorem · general topology
BoundedContinuousFunction.dist_eq_iSup
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
{f g : BoundedContinuousFunction α β}, dist f g = ⨆ x, dist (f x) (g x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- iSupstatement · cited by 2,415
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- IsEmptyproof · cited by 759
- BoundedContinuousFunctionstatement and proof · cited by 511
- LE.le.antisymmproof · cited by 507
- isEmpty_or_nonemptyproof · cited by 269
- Set.forall_mem_rangeproof · cited by 135
- le_ciSupproof · cited by 57
Cited by3
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.norm_eq_iSup_normproof · cited by 5
- BoundedContinuousFunction.nndist_eq_iSupproof · cited by 2
- ContinuousMap.dist_eq_iSupproof · cited by 0