Theorems · Theorem · general topology
UniformOnFun.uniformContinuous_ofFun_toFun_of_mem
∀ {α : Type u_1} (β : Type u_2) [inst : UniformSpace β] (𝔖 : Set (Set α)),
∀ s ∈ 𝔖, UniformContinuous (⇑(UniformOnFun.ofFun 𝔖) ∘ ⇑(UniformOnFun.toFun {s}))A specialized version of UniformOnFun.uniformContinuous_ofFun_toFun for convenience.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- UniformSpacestatement and proof · cited by 2,040
- UniformContinuousstatement · cited by 410
- UniformOnFunstatement · cited by 150
- UniformOnFun.toFunstatement · cited by 87
- UniformOnFun.ofFunstatement · cited by 63
- UniformOnFun.uniformContinuous_ofFun_toFun_of_subsetproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- continuousOn_cfcₙ_setProd_nhdsSetproof · cited by 0
- continuousOn_cfc_setProd_nhdsSetproof · cited by 0
- continuousOn_cfcₙ_nnreal_setProd_nhdsSetproof · cited by 0
- continuousOn_cfc_nnreal_setProd_nhdsSetproof · cited by 0