A note on -compact spaces
Author: Teklehaimanot Retta
Journal: Proc. Amer. Math. Soc. 89 (1983), 314-316
MSC: Primary 54B10; Secondary 03E55, 54D60
MathSciNet review: 712643
Abstract: For an infinite cardinal , denotes the least measurable cardinal, if one exists, not less than . We give easy proofs of generalizations of some results on realcompact spaces. Among these we prove the following generalization of a theorem of A. Kato.
Let be a collection of spaces each having at least two elements. Then the -box product is -compact if and only if either is -compact for each and or .
-  W. Wistar Comfort and Teklehaimanot Retta, Generalized perfect maps and a theorem of I. Juhász, Rings of continuous functions (Cincinnati, Ohio, 1982) Lecture Notes in Pure and Appl. Math., vol. 95, Dekker, New York, 1985, pp. 79–102. MR 789263
-  Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
-  Akio Kato, Realcompactness of box products, Mem. Defense Acad. 19 (1979), no. 1, 1–4. MR 532792
-  T. Retta, Doctoral Dissertation, Wesleyan University, 1977.
- W. W. Comfort and T. Retta, Generalized perfect maps and a theorem of I. Juhász (preprint). MR 789263 (87e:54001)
- L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
- A. Kato, Realcompactness of box products, Mem. Defense Acad. Japan 19 (1979), 1-4. MR 532792 (80h:54032)
- T. Retta, Doctoral Dissertation, Wesleyan University, 1977.
Keywords: -compact space, measurable cardinal, box topology, -box topology, -base
Article copyright: © Copyright 1983 American Mathematical Society