Theorems · Theorem · general topology
UniformFun.uniformContinuous_eval
∀ {α : Type u_1} (β : Type u_2) [inst : UniformSpace β] (x : α), UniformContinuous (Function.eval x ∘ ⇑UniformFun.toFun)Evaluation at a fixed point is uniformly continuous on α →ᵤ β.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Equivstatement · cited by 8,337
- UniformSpacestatement and proof · cited by 2,040
- uniformityproof · cited by 765
- UniformContinuousstatement · cited by 410
- Function.evalstatement and proof · cited by 140
- UniformFunstatement and proof · cited by 106
- Filter.basis_setsproof · cited by 105
- Filter.HasBasis.comapproof · cited by 89
- UniformFun.toFunstatement and proof · cited by 47
- Filter.HasBasis.le_basis_iffproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- UniformOnFun.uniformContinuous_eval_of_memproof · cited by 4
- UniformFun.uniformContinuous_toFunproof · cited by 2