부산대학교 도서관

The author gives results characterizing the smallest closed semi-algebra [semi-algebra of type 1], containing a given finite set $\{f_1,\cdots,f_n\}$ of elements of $\scr C(X)$, where $X$ is a locally compact Hausdorff space, and $\scr C(X)$ is equipped with the compact-open topology. When $X$ is compact, that semi-algebra consists of all functions of the form $\varphi\circ(f_1,\cdots,f_n)$, where $\varphi$ belongs to $\scr C(R^n)$, is increasing [sub-homogeneous] and vanishes at the origin.