#### Title

Almost Discrete SV-Spaces

#### 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*_{∞}={ƒε*C*(*X*):ƒ(∞)=0} contains only finitely many minimal prime ideals. Some unsolved problems are posed.

#### Rights Information

© 1992 Elsevier

#### Terms of Use & License Information

#### 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.