Theorems · Theorem · general topology
UniformContinuous.continuous
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
UniformContinuous f → Continuous f- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 66 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
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.
- Continuousstatement · cited by 2,592
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement and proof · cited by 410
- continuous_iff_le_inducedproof · cited by 16
- uniformContinuous_iff_le_comapproof · cited by 9
- UniformSpace.toTopologicalSpace_monoproof · cited by 2
Cited by66
Results whose statement or proof uses this declaration.
- LipschitzWith.continuousproof · cited by 30
- continuous_distproof · cited by 9
- AbstractCompletion.extend_coeproof · cited by 8
- MvPowerSeries.coe_eval₂Homproof · cited by 5
- AbstractCompletion.continuous_extendproof · cited by 5
- Seminorm.continuous_of_continuousAt_zeroproof · cited by 4
- NormedAddGroupHom.continuousproof · cited by 4
- MvPowerSeries.continuous_eval₂proof · cited by 4
- continuous_nndistproof · cited by 4
- UniformContinuousOn.continuousOnproof · cited by 3
- UniformSpace.Completion.continuous_distproof · cited by 3
- Isometry.mapRingHom_coeproof · cited by 2