 Conic hull

The set of all finite conic combinations of elements of $S$, including zero. It is the smallest convex cone containing $S$. It need not be closed even when $S$ is closed: the closed set $S=\{(t,1):t\ge 1\}$ generates vectors converging to $(1,0)$ via $(t,1)/t$, but no nonzero generated vector has second coordinate zero.