Definition:Closure (Abstract Algebra)/Scalar Product

Definition
Let $\left({S, \circ}\right)_R$ be an $R$-algebraic structure.

Let $T \subseteq S$ such that $\forall \lambda \in R: \forall x \in T: \lambda \circ x \in T$.

Then $T$ is closed for scalar product.

If $T$ is also closed for operations on $S$, then it is called a closed subset of $S$.