Theorems · Theorem · general topology
UniformSpace.Completion.uniformContinuous_dist
∀ {α : Type u} [inst : PseudoMetricSpace α], UniformContinuous fun p => dist p.1 p.2The new distance is uniformly continuous.
- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- UniformContinuousstatement · cited by 410
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.uniformContinuous_extension₂proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.continuous_distproof · cited by 3
- UniformSpace.Completion.mem_uniformity_distproof · cited by 0