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Continuous Preimages of Spaces with Finite Compactifications

Published online by Cambridge University Press:  20 November 2018

George L. Cain Jr.
George L. Cain Jr.*
Affiliation:
School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332, U.S.A.
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A compactification αX of the space X is called an n -point compactification if the remainder αX — X consists of exactly n points. K. D. Magill [5] showed that if Y has an n-point compactification and if f:X→ f(x) = Y is a compact continuous mapping of the space X onto Y, then X also has an n-point compactification.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 177 - 180
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Cain, G. L. Jr, Compact and related mappings, Duke Math. J.. 33 (1966), 639-645.Google Scholar
2. Cain, G. L. Jr, Compactification of mappings, Proc. Amer. Math. Soc.. 23 (1969), 298-303.Google Scholar
3. Chandler, R. E., Hausdorff Compactifications, Marcel Dekker, Inc., New York and Basel, 1976.Google Scholar
4. Choo, E. U., Accumulation points of continuous real-valued functions and compactifications, Canad. Math. Bull.. 20 (1977), 47-52.Google Scholar
5. Magill, K. D. Jr, N-point compactifications, Amer. Math. Monthly. 72 (1965), 1075-1081.Google Scholar
6. Whyburn, G. T., Compactification of mappings, Math. Ann.. 166 (1966), 168-174.Google Scholar
7. Whyburn, G. T., A unified space for mappings, Trans. Amer. Math. Soc.. 74 (1953), 344-350.Google Scholar