Almost Discrete SV-Spaces

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
R. G. Wilson, Universidad Autónoma Metropolitana

Document Type

Article

Department

Mathematics (HMC)

Publication Date

9-29-1992

Abstract

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.

Rights Information

© 1992 Elsevier

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/0166-8641(92)90123-H

Recommended Citation

Henriksen, M. and Wilson, R. G. 1992. Almost discrete SV-spaces. Topology and its Applications. 46(2):89-97.