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Hausdorff Compactifications as Epireflections

Published online by Cambridge University Press:  20 November 2018

W. N. Hunsaker  and
S. A. Naimpally
W. N. Hunsaker
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
S. A. Naimpally
Affiliation:
Department of Mathematics, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1
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Abstract

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We answer the following problem posed by Herrlich in the affirmative: “Can the Freudenthal compactification be regarded as a reflection in a sensible way?” This is accomplished by exploiting the one-to-one correspondence between proximities compatible with a given Tihonov space and compactifications of that space. We give topological characterizations of proximally continuous functions for the proximities associated with the Freudenthal and Fan-Gottesman compactifications.

Keywords

54C1054D3554E0554E1018A4018A9954D30Proximity spaceproximally continuousFreudenthal compactificationepireflectionsemi-compactFan-Gottesman compactification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 675 - 677
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Dickman, R. F. Jr, Some characterizations of the Freudenthal compactification of a semicompact space, Proc. Amer. Math. Soc. 19 (1968), 631–633.Google Scholar
2. Fan, K. and Gottesman, N., On compactifications of Freudenthal and Wallman, Indag. Math. 14 (1952), 504–510.Google Scholar
3. Freudenthal, H., Kompaktisierungen und Bikompaktisierungen, Indag. Math. 13 (1951) 184–192.Google Scholar
4. Herrlich, H., Categorical Topology, General Topology and Applications 1 (1971), 1–15.Google Scholar
5. Morita, K., On bicompactifications of semibicompact spaces, Sci. Rep. Tokyo Bunrika Daigaku Sect. A 4 (1952), 222–229.Google Scholar
6. Naimpally, S. A. and Warrack, B. D., Proximity Spaces, Cambridge Tract in Mathematics and Mathematical Physics No. 59, Cambridge University Press (1970).Google Scholar
7. Smirnov, Y. M., On proximity spaces, Math. Sb. 31 (73) (1952), 543–574; English translation in Amer. Math. Soc. Transi. (2) 38 (1964), 5–36.Google Scholar