Theorems · Definition · general topology
UniformOnFun
(α : Type u_1) → Type u_2 → Set (Set α) → Type (max u_1 u_2)
The type of functions from α to β equipped with the uniform structure and topology of
uniform convergence on some family 𝔖 of subsets of α. We denote it α →ᵤ[𝔖] β.
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by160
Results whose statement or proof uses this declaration.
- UniformOnFun.toFunstatement · cited by 87
- UniformOnFun.ofFunstatement and proof · cited by 63
- UniformOnFun.genstatement and proof · cited by 18
- ContinuousMap.isUniformEmbedding_toUniformOnFunIsCompactstatement · cited by 8
- ContinuousMap.toUniformOnFunIsCompactstatement · cited by 8
- ContinuousMultilinearMap.toUniformOnFunstatement · cited by 7
- UniformOnFun.tendsto_iff_tendstoUniformlyOnstatement and proof · cited by 5
- UniformConvergenceCLM.isEmbedding_coeFnstatement · cited by 5
- UniformOnFun.hasBasis_uniformity_of_basisstatement · cited by 4
- UniformOnFun.postcomp_isUniformInducingstatement and proof · cited by 4
- UniformOnFun.uniformContinuous_eval_of_memstatement · cited by 4
- UniformOnFun.uniformContinuous_ofFun_toFun_of_memstatement · cited by 4