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Almost-P-Spaces

Published online by Cambridge University Press:  20 November 2018

Ronnie Levy
Ronnie Levy*
Affiliation:
George Mason University, Fairfax, Virginia
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Abstract

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A P-space is a topological space in which every Gδ-set is open. P-spaces are fairly rare. For example, the only compact (or even pseudocompact) P-spaces are finite. A larger class of spaces, the almost-P-spaces, consists of those spaces in which G δ-sets have dense interiors. The almost-P-spaces are far less restricted than the P-spaces—for example, there are infinite, compact, connected almost-P-spaces. In this paper, we study almost-P-spaces and raise a number of questions relating to them.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 284 - 288
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Cohen, P. J., Set theory and the continuum hypothesis (>W. A. Benjamin, 1966).W.+A.+Benjamin,+1966).>Google Scholar
2. Fine, N. J. and Gillman, L., Extensions of continuous finctions in β N, Bull. Amer. Math. Soc. 66 (1960), 376–381.Google Scholar
3. Gillman, L., and Jerison, M., Rings of continuous functions (Van Nostrand, 1960).Google Scholar
4. Levy, R., Non-Blumberg Baire spaces and related topics, Thesis, Washington University, 1974.Google Scholar
5. Levy, R. Showering spaces, Pac. J. Math. 57 (1975), 223–232.Google Scholar
6. Levy, R. Strongly non-Blumberg spaces, Gen. Top. App. 4 (1974), 173–177.Google Scholar
7. Mrowka, S., On the potency of compact spaces and the first axiom of countability, Bull. Acad. Polon. Sci., Ser. Math. Ast. Phys. 6 (1958), 7–9.Google Scholar
8. Plank, D., On a class of subalgebras of C(X) with applications to (3X — X, Fund. Math. 64 (1969), 41–54.Google Scholar
9. Rudin, W., Homogeneity problems in the theory of Cech compactifications, Duke Math. J. 23 (1956), 409–419.Google Scholar
10. Smirnov, Yu. M., On the ring of bounded continuous functions over a normal space, Mat. Sbornik N.S. 30 (72) (1952), 213–218 (Russian).Google Scholar
11. Veksler, A. I., P'-points, P'-sets, P'-spaces: A new class of order-continuous measures and functionals, Sov. Math. Dokl. 14 (1973), 1445–1450 (Eng. Trans.).Google Scholar
12. Walker, R. C., The Stone-Cech compactification (Springer-Verlag, 1974).Google Scholar
13. White, H. E., Blumberg's theorem in topological spaces, Proc. Amer. Math. Soc. 44 (1974), 454–462.Google Scholar