Abstract
An abstract concept of (D, H)-analytic sets is introduced and applied to characterizations of normality, perfect normality and Oz-spaces, as well as to some problems related to the theory of compactifications. A metrization theorem for pseudocompact spaces is deduced.
Similar content being viewed by others
REFERENCES
W. Adamski, On the interplay between a topology and its associated Baire and Borel σ-algebra, Period. Math. Hungarica 21 (1990), 85–93.
R. L. Blair, Spaces in which special sets are z-embedded, Canad. J. Math. 28 (1976), 673–690.
R. L. Blair and M. A. Swardson, Spaces with an Oz Stone Čech compactification, Topology Appl. 36 (1990), 73–92.
J. L. Blasco, Hausdorff compactifications and Lebesgue sets, Topology Appl. 15 (1983), 111–117.
J. Chaber, Conditions which imply compactness in countably compact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 993–998.
R. O. Davies, J. E. Jayne, A. J. Ostaszewski and C. A. Rogers, Theorems of Novikov type, Mathematika 24 (1977), 97–114.
B. Diamond, Algebraic subrings and perfect compactifications, Topology Appl. 39 (1991), 217–228.
R. Engelking, General Topology, Heldermann, 1984.
L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, 1976.
L. Glicksberg, Stone-Čech compactification of products, Trans. Amer. Math. Soc. 90 (1959), 369–382.
G. Gruenhage, Generalized metric spaces, Chapter 10 in “Handbook of Set-Theoretic Topology”, (K. Kunen and J. E. Vaughan, Editors), North-Holland, 1984, 423–501.
K. Kunen and J. E. Vaughan, Editors, Handbook of Set-Theoretic Topology, North-Holland, 1984.
M. Morayne, Complements of sets in abstract Borelian hierarchies, Topology Appl. 39 (1991), 277–281.
C. A. Rogers ET AL., Analytic Sets, London Academic Press, 1980.
E. Wajch, Compactifications and L-separation, Comment. Math. Univ. Carolinae 29 (1988), 477–484.
E. Wajch, Pseudocompactness — from compactifications to multiplication of Borel sets, Colloq. Math. 63 (1992), 303–309.
E. Wajch, A little more on the product of two pseudocompact spaces, Colloq. Math. 71 (1996), 31–42.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wajch, E. On (D,H)-analytic Sets and their Topological Applications. Periodica Mathematica Hungarica 34, 235–248 (1997). https://doi.org/10.1023/A:1004375522666
Issue Date:
DOI: https://doi.org/10.1023/A:1004375522666