continuousSubring — Mathlib

English

The continuous maps α → R form a subring of the function space α → R when R is a topological ring with IsTopologicalRing.

Русский

Непрерывные отображения α → R образуют подп ring пространства функций, когда R - топологическая кольцо.

LaTeX

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

Lean4

/-- The subring of continuous maps `α → β`. -/
def continuousSubring (α : Type*) (R : Type*) [TopologicalSpace α] [TopologicalSpace R] [Ring R] [IsTopologicalRing R] :
    Subring (α → R) :=
  { continuousAddSubgroup α R, continuousSubsemiring α R with }

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