C(X) Can Sometimes Determine X Without X Being Realcompact

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Biswajit Mitra, University of Calcutta

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2005

Abstract

As usual C(X) will denote the ring of real-valued continuous functions on a Tychonoff space X. It is well-known that if X and Y are realcompact spaces such that C(X) and C(Y ) are isomorphic, then X and Y are homeomorphic; that is C(X) determines X. The restriction to realcompact spaces stems from the fact that C(X) and C(uX) are isomorphic, where uX is the (Hewitt) realcompactifcation of X. In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact spaces is exhibited such that C(X) determines X. The problem of getting similar results for other restricted classes of generalized realcompact spaces is posed.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,443.

Publisher pdf, posted with permission.

Article can also be found at http://dml.cz/dmlcz/119561

Rights Information

© 2005 Charles University in Prague

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Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Henriksen, Melvin, and Biswajit Mitra. "C(X) can sometimes determine X without X being realcompact." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 711-720.