topologicalSpace — Mathlib

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

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