Definition:Closed


 * Closed set: In topology, a subset of a topological space which contains all its limit points.


 * Closed walk: In graph theory, a walk whose first vertex is the same as the last.


 * An algebraic structure $$\left({S, \circ}\right)$$ is closed iff $$\forall \left({x, y}\right) \in S \times S: x \circ y \in S$$.


 * A subset $$T \subseteq S$$ of an $R$-algebraic structure $$\left({S: \circ}\right)_R$$ is closed for scalar product iff $$\forall \lambda \in R: \forall x \in T: \lambda \circ x \in T$$.