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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

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