Theorems · Theorem · general topology
uniformContinuous_of_const
∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] {c : α → β},
(∀ (a b : α), c a = c b) → UniformContinuous c- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- UniformSpacestatement and proof · cited by 2,040
- le_transproof · cited by 985
- uniformityproof · cited by 765
- Filter.principalproof · cited by 740
- UniformContinuousstatement · cited by 410
- Set.eq_univ_iff_forallproof · cited by 93
- Filter.comap_principalproof · cited by 47
- Filter.principal_univproof · cited by 46
- SetRel.idproof · cited by 33
- Filter.map_le_iff_le_comapproof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- uniformContinuous_constproof · cited by 21
- AbstractCompletion.uniformContinuous_extendproof · cited by 5
- SeparationQuotient.uniformContinuous_lift'proof · cited by 1
- CauchyFilter.uniformContinuous_extendproof · cited by 0