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ℒ-Realcompactifications and Normal Bases

Published online by Cambridge University Press:  09 April 2009

R. A. Alo  and
H. L. Shapiro
R. A. Alo
Affiliation:
The Carnegie Institute of Technology The Pennsylvania State University
H. L. Shapiro
Affiliation:
The Carnegie Institute of Technology The Pennsylvania State University
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In a recent paper (see [2]), Orrin Frink introduced a method to provide Hausdorff compactifications for Tychonoff or completely regular T1 spaces X. His method utilized the notion of a normal base. A normal base ℒ for the closed sets of a space X is a base which is a disjunctive ring of sets, disjoint members of which may be separated by disjoint complements of members of ℒ.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 489 - 495
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Alo, R. A. and Shapiro, H. L., ‘A note on compactifications and semi-normal spaces’, J. Austral. Math. Soc. 8 (1968), 102–108.CrossRefGoogle Scholar
[2]Frink, Orrin, ‘Compactifications and semi-normal spaces’, Amer. J. Math. 86 (1964), 602–607.Google Scholar
[3]Gillman, L. and Jerison, M., Rings of continuous functions. (New York: Van Nostrand, 1960.)Google Scholar