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Every Hausdorff Compactification of a Locally Compact Separable Space is a Ga Compactification

Published online by Cambridge University Press:  20 November 2018

J. Van Mill
J. Van Mill*
Affiliation:
Free University, Amsterdam, The Netherlands
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Abstract

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In [4], De Groot and Aarts constructed Hausdorff compactifications of topological spaces to obtain a new intrinsic characterization of complete regularity. These compactifications were called GA compactifications in [5] and [7]. A characterization of complete regularity was earlier given by Frink [3], by means of Wallman compactifications, a method which led to the intriguing problem of whether every Hausdorff compactification is a Wallman compactification.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 125 - 131
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Aarts, J. M., Every metric compactification is a Wallman-type compactification, Proc. Int. Symp. on Topology and its Applications (Herceg-Novi, Yugoslavia, 1968).Google Scholar
2. Berney, E. S., On Wallman compactifications, Notices Amer. Math. Soc. 17, (1970), 215.Google Scholar
3. Frink, O., Compactifications and semi-normal spaces, Amer. J. Math. 86 (1964), 602–607.Google Scholar
4. De Groot, J. and Aarts, J. M., Complete regularity as a separation axiom, Can. J. Math. 21 (1969), 96–105.Google Scholar
5. De Groot, J., Hursch, J. L. and Jensen, G. A., Local connectedness and other properties of G A compactifications, Indag. Math. 34 (1972), 11–18.Google Scholar
6. De Groot, J., Jensen, G. A. and Verbeek, A., Superextensions, Report, Mathematical Centre ZW 1968–107, Amsterdam (1968).Google Scholar
7. Hursch, J. L., The local connectedness of G A compactifications generated by all closed connected sets, Indag. Math. 33 (1971), 411–417.Google Scholar
8. Juhâsz, I., Cardinal functions in topology, Mathematical Centre Tracts 34, Mathematisch Centrum, Amsterdam (1975).Google Scholar
9. van Mill, J., On super compactness and superextensions, rapport 37, Wiskundig Seminariuin der Vrije Universiteit, Amsterdam (1975).Google Scholar
10. Steiner, A. K. and Steiner, E. F., Products of compact metric spaces are regular Wallman, Indag. Math. 30 (1968), 428–430.Google Scholar
11. Steiner, E. F., Wallman spaces and compactifications, Fund. Math. 61 (1968), 295–304.Google Scholar
12. Verbeek, A., Superextensions of topological spaces, Mathematical Centre Tracts, 41 Mathematisch Centrum, Amsterdam (1972).Google Scholar