Theorems · Theorem · general topology
UniformSpace.Completion.continuous_dist
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : TopologicalSpace β]
{f g : β → UniformSpace.Completion α}, Continuous f → Continuous g → Continuous fun x => dist (f x) (g x)The new distance is continuous.
- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Continuousstatement and proof · cited by 2,592
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Continuous.compproof · cited by 371
- UniformSpace.Completionstatement and proof · cited by 192
- Continuous.prodMkproof · cited by 127
- UniformContinuous.continuousproof · cited by 66
- UniformSpace.Completion.uniformContinuous_distproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.dist_commproof · cited by 1
- UniformSpace.Completion.dist_selfproof · cited by 1
- UniformSpace.Completion.dist_triangleproof · cited by 0