English
The topology on the function space α →ᵤ β is the topology induced by the uniform convergence structure; equivalently, the space α →ᵤ β carries a natural topological structure arising from the uniform convergence notion.
Русский
У пространства функций α →ᵤ β существует естественная топология, индуцированная понятием равномерной конвергенции.
LaTeX
$$$$\text{Top}(\alpha \to^{u} \beta)\; =\; \text{the topology induced by the uniform convergence structure on } \alpha \to^{u} \beta.$$$$
Lean4
/-- Topology of uniform convergence, declared as an instance on `α →ᵤ β`. -/
instance topologicalSpace : TopologicalSpace (α →ᵤ β) :=
inferInstance