Almost Discrete SV-Spaces

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Mathematics (HMC)

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A 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.

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© 1992 Elsevier

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