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A Class of Function Algebras

Published online by Cambridge University Press:  20 November 2018

F. W. Anderson
F. W. Anderson*
Affiliation:
University of Oregon
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A problem which has generated considerable interest during the past couple of decades is that of characterizing abstractly systems of realvalued continuous functions with various algebraic or topological-algebraic structures. With few exceptions known characterizations are of systems of bounded continuous functions on compact or locally compact spaces. Only recently have characterizations been given of the systems C(X) of all realvalued continuous functions on an arbitrary completely regular space X (1). One of the main objects of this paper is to provide, by using certain special techniques, a characterization of C(X) for a particular class of (not necessarily compact) completely regular spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 353 - 362
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Anderson, F.W. and Blair, R.L., Characterizations of the algebra of all real-valued continuous functions on a completely regular space, Illinois J. Math., 3 (1959), 121–133.Google Scholar
2. Birkhoff, G., Lattice theory (rev. éd., New York, 1948).Google Scholar
3. Birkhoff, G. and Pierce, R.S., Lattice-ordered rings, An. Acad. Brasil. Ci., 28 (1956), 41–69.Google Scholar
4. Brainerd, B., On a class of latttice-ordered rings, Proc. Amer. Math. Soc, 8 (1957), 673–683.Google Scholar
5. Brainerd, B. F-rings of continuous functions I, Can. J. Math., 11 (1959), 80–86.Google Scholar
6. Fan, K., Partially ordered additive groups of continuous functions, Ann. Math., 51 (1950), 409–427.Google Scholar
7. Gillman, L. and Henriksen, M., Concerning rings of continuous functions, Trans. Amer. Math. Soc, 77 (1954), 340–362.Google Scholar
8. Halmos, P. R, Measure theory (New York, 1950).Google Scholar
9. Hewitt, E., Rings of real-valued continuous functions. I Trans. Amer. Math. Soc, 64 (1948), 45–99.Google Scholar
10. Kakutani, S., Concrete representation of abstract (M)-spaces, Ann. Math., 42 (1941), 994–1024.Google Scholar
11. Nakano, H., Modern spectral theory (Tokyo, 1950).Google Scholar
12. von Neumann, J., Regular rings, Proc Nat. Acad. Sci. U.S.A., 22 (1936), 707–713.Google Scholar
13. Stone, M.H., A general theory of spectra. II, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 83–87.Google Scholar