Abstract
This article studies the properties of various subclasses of weakly dyadic compact spaces. We prove that each weakly dyadic compact space is a strictly \( a \)-space. We also show that the product of a compact space and a Corson compact space without isolated points is a strictly \( a \)-space.
Similar content being viewed by others
References
Mrówka S., “Mazur theorem and \( m \)-adic spaces,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., no. 18, 299–305 (1970).
Kulpa W. and Turzański M., “Bijections onto compact spaces,” Acta Univ. Carolin. Math. Phys., vol. 29, no. 2, 43–49 (1988).
Bell M.G., “Generalized dyadic spaces,” Fund. Math., vol. 125, no. 1, 47–58 (1985).
Belugin V.I., “Contractions onto bicompacta,” Soviet Math. Dokl., vol. 13, no. 2, 1481–1483 (1972).
Belugin V.I., “Contractions onto bicompacta,” C. R. Acad. Bulgare Sci., vol. 28, no. 11, 1447–1449 (1975).
Belugin V.I., “Condensations onto bicompact sets of subspaces of ordered bicompacta,” in: Topology and Theory of Sets, RKhD, Izhevsk (1982), 3–8 [Russian].
Belugin V.I., “Condensations on bicompacta and products of spaces,” in: Cardinal Invariants and Extensions of Topological Spaces, RKhD, Izhevsk (1989), 36–43 [Russian].
Belugin V.I., Osipov A.V., and Pytkeev E.G., “On classes of subcompact spaces,” Math. Notes, vol. 109, no. 6, 849–858 (2021).
Belugin V.I., Osipov A.V., and Pytkeev E.G., “Compact condensations of Hausdorff spaces,” Acta Math. Hungar., vol. 164, no. 1, 15–27 (2021).
Belugin V.I., Osipov A.V., and Pytkeev E.G., “Some properties of subcompact spaces,” Math. Notes, vol. 111, no. 2, 193–203 (2022).
Osipov A.V. and Pytkeev E.G., “On the problem of condensation onto compact spaces,” Dokl. Math., vol. 100, no. 2, 430–432 (2019).
Osipov A.V. and Pytkeev E.G., “Solution of Ponomarev’s problem of condensation onto compact sets,” Sib. Math. J., vol. 62, no. 1, 131–137 (2021).
Aleksandrov P.S., “On some basic directions in general topology,” Russian Math. Surveys, vol. 19, no. 6, 1–39 (1964).
Moore R.L., Foundations of Point Set Theory. Amer. Math. Soc. Colloquium Publ.; XIII, Amer. Math. Soc., New York (1932).
Turzański M., “On generalizations of dyadic spaces,” Acta Univ. Carolin. Math. Phys., vol. 30, no. 2, 153–159 (1989).
Arkhangelskii A.V., “Approximation of the theory of didactic bicompacta,” Dokl. Akad. Nauk SSSR, vol. 184, no. 4, 767–770 (1969).
Engelking R., “On closed images of the space of irrationals,” Proc. Amer. Math. Soc., no. 21, 583–586 (1969).
Aleksandrov P.S. and Urysohn P.S., “On compact topological spaces,” Trudy Mat. Inst. Steklov., no. 31, 3–95 (1950).
Efimov B.A., “Metrizability and the \( \sum \)-product of bicompacta,” Dokl. Akad. Nauk SSSR, vol. 152, no. 4, 794–797 (1963).
Parkhomenko A.S., “On condensations to compact spaces,” Izv. Akad. Nauk SSSR. Ser. Mat., vol. 5, no. 3, 225–232 (1941).
Iliadis S., “Certain properties of absolutes,” Soviet Math. Dokl., vol. 152, no. 4, 1409–1411 (1963).
Arhangel’skii A.V., “I. Compactness,” in: General Topology II. Compactness, Homologies of General Spaces. Encyclopaedia Math. Sci., vol. 50, Springer, Berlin etc. (1996), 4–117.
Acknowledgment
The authors are grateful to the referee for useful remarks.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 6, pp. 1204–1212. https://doi.org/10.33048/smzh.2022.63.602
Rights and permissions
About this article
Cite this article
Belugin, V.I., Osipov, A.V. & Pytkeev, E.G. On the Properties of Subclasses of Weakly Dyadic Compact Spaces. Sib Math J 63, 1034–1040 (2022). https://doi.org/10.1134/S0037446622060027
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446622060027