Almost discrete SV-spaces

AbstractA Hausdorff space is called almost discrete if it has precisely one nonisolated point. A Tychonoff space Y is called an SV-space if C(Y)P is a valuation ring for every prime ideal P of C(Y). it is shown that the almost discrete space X=D∪{∞} is an SV-space if and only if X is a union of finitely many closed basically disconnected subspaces if and only if M∞={ƒϵC(X):ƒ(∞)=0} contains only finitely many minimal prime ideals. Some unsolved problems are posed