continuousSubsemiring — Mathlib

English

The set of continuous maps α → R forms a subsemiring of the function space α → R when α, R have appropriate topologies and R is a semiring with IsTopologicalSemiring.

Русский

Множество непрерывных отображений α → R образует подпредпосемирий пространства функций при наличии подходящих топологий и полейентика.

LaTeX

$$$\text{continuousSubsemiring}(α,R)\subseteq (α\to R)$$$

Lean4

/-- The subsemiring of continuous maps `α → β`. -/
def continuousSubsemiring (α : Type*) (R : Type*) [TopologicalSpace α] [TopologicalSpace R] [NonAssocSemiring R]
    [IsTopologicalSemiring R] : Subsemiring (α → R) :=
  { continuousAddSubmonoid α R, continuousSubmonoid α R with }

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