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General rings of functions

Published online by Cambridge University Press:  09 April 2009

A. Sultan
A. Sultan
Affiliation:
Queens CollegeFlushing, New York 11367.
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Several authors have studied various types of rings of continuous functions on Tychonoff spaces and have used them to study various types of compactifications (See for example Hager (1969), Isbell (1958), Mrowka (1973), Steiner and Steiner (1970)). However many important results and properties pertaining the Stone-Čech compactification and the Hewitt realcompactification can be extended to a more general setting by considering appropriate lattices of sets, generalizing that of the lattice of zero sets in a Tychonoff space. This program was first considered by Wallman (1938) and Alexandroff (1940) and has more recently appeared in Alo and Shapiro (1970), Banachewski (1962), Brooks (1967), Frolik (1972), Sultan (to appear) and others.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 359 - 365
Copyright
Copyright © Australian Mathematical Society 1975

References

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