Theorems · Theorem · general topology
ContinuousMap.dist_eq_iSup
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : CompactSpace α] [inst_2 : PseudoMetricSpace β]
{f g : C(α, β)}, dist f g = ⨆ x, dist (f x) (g x)- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- ContinuousMapstatement and proof · cited by 2,491
- iSupstatement and proof · cited by 2,415
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- CompactSpacestatement and proof · cited by 593
- ContinuousMap.isometryEquivBoundedOfCompactproof · cited by 8
- IsometryEquiv.dist_eqproof · cited by 6
- BoundedContinuousFunction.dist_eq_iSupproof · cited by 3
- ContinuousMap.isometryEquivBoundedOfCompact_applyproof · cited by 3
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