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Accumulation Points of Continuous Realvalued Functions and Compactifications

Published online by Cambridge University Press:  20 November 2018

Eng Ung Choo
Eng Ung Choo*
Affiliation:
Department of Mathematics, University of British Columbia, VancouverB.C.
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All topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions on X. βX is the Stone-Cech compactification of X. A real number t is said to be an accumulation point of a function f ∊ C(X) if and only if f-1[[t-ε, t + ε]] is not compact for every ε > 0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 47 - 52
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Choo, E. U., Admissible Subrings of Real-valued Functions, Doctoral Thesis, The University of British Columbia, Canada. 1971.Google Scholar
2. Firby, P. A., Lattice and Compactifications, III. London Mathematical Society Proceedings Ser. 3, Vol. 27 (1973), 61-68.Google Scholar
3. Gillman, L. and Jerison, M., Rings of Continuous Functions, Van Nostrant, N.Y., 1960.Google Scholar
4. Loeb, P. A., Compactifications of Hausdorff Spaces, Proc. Amer. Math. Soc. 22 (1969), 627-634.Google Scholar
5. Loeb, P. A., A Minimal Compactification for Extending Functions, Proc. Amer. Math. Soc. 18 (1967), 282-283.Google Scholar
6. Magill, K. D. Jr., N-point Compactifications, Amer. Math. Monthly 72 (1965), 1075-1081.Google Scholar
7. Magill, K. D. Jr.,Countable Compactifications, Canad. J. Math. 18 (1966), 616-620.Google Scholar