Theorems · Theorem · general topology
BoundedContinuousFunction.dist_coe_le_dist
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
{f g : BoundedContinuousFunction α β} (x : α), dist (f x) (g x) ≤ dist f gThe pointwise distance is controlled by the distance between functions, by definition.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 117 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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- BoundedContinuousFunctionstatement and proof · cited by 511
- le_csInfproof · cited by 36
- BoundedContinuousFunction.dist_set_existsproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.norm_coe_le_normproof · cited by 25
- BoundedContinuousFunction.dist_leproof · cited by 11
- BoundedContinuousFunction.dist_eq_iSupproof · cited by 3
- BoundedContinuousFunction.dist_le_iff_of_nonemptyproof · cited by 3
- MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimateproof · cited by 2
- BoundedContinuousFunction.nndist_coe_le_nndistproof · cited by 2
- BoundedContinuousFunction.tendsto_iff_tendstoUniformlyproof · cited by 2
- BoundedContinuousFunction.dist_lt_iff_of_compactproof · cited by 2
- BoundedContinuousFunction.lipschitz_compproof · cited by 2
- BoundedContinuousFunction.lipschitz_compContinuousproof · cited by 2
- BoundedContinuousFunction.NNReal.upper_boundproof · cited by 1
- BoundedContinuousFunction.dist_extend_extendproof · cited by 1