Theorems · Theorem · general topology
uniformContinuous_sInf_rng
∀ {α : Type ua} {β : Type ub} {f : α → β} {u₁ : UniformSpace α} {u₂ : Set (UniformSpace β)},
UniformContinuous f ↔ ∀ u ∈ u₂, UniformContinuous f- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterproof · cited by 8,121
- Filter.Tendstoproof · cited by 3,814
- UniformSpacestatement and proof · cited by 2,040
- InfSet.sInfstatement · cited by 935
- uniformityproof · cited by 765
- UniformContinuousstatement · cited by 410
- iInf_uniformityproof · cited by 19
- sInf_eq_iInf'proof · cited by 17
- Filter.tendsto_iInfproof · cited by 13
- SetCoe.forallproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- isUniformAddGroup_sInfproof · cited by 1
- isUniformGroup_sInfproof · cited by 1