Abstract
In this paper, it is proved that if a covariant functor ℱ: Comp → Comp is weakly normal, then d(ℱβ(X)) ≤ d(X) and wd(ℱβ(X)) ≤ wd(X) for any infinite Tychonoff space X.
Similar content being viewed by others
References
E. V. Shchepin, “Functors and uncountable degrees of compacta,” UspekhiMat. Nauk 36(3), 3–62 (1981).
M. M. Zarichnyi, “On properties of normal functors,” in V Tiraspol Symposium on General Topology and Its Applications, Tiraspol, USSR, 1985 (Shtiintsa, Kishinev, 1985), pp. 96–97.
A. Ch. Chigogidze, “Extension of normal functors,” VestnikMoskov. Univ. Ser. I Mat. Mekh., No. 6, 23–26 (1984).
A. V. Arkhangel’skii and V. I. Ponomarev, Fundamentals of General Topology through Problems and Exercises (Nauka, Moscow, 1974) [in Russian].
R. B. Beshimov, “Some cardinal properties of topological spaces connected with weak density,” Methods Funct. Anal. Topology 10(3), 17–22 (2004).
R. B. Beshimov, “A note on weakly separable spaces,” Math. Morav. 6, 9–19 (2002).
B. B. Fedorchuk and V. V. Filippov, General Topology: Basic Constructions (Mosk. Gos. Univ., Moscow, 1988) [in Russian].
V. V. Fedorchuk and S. Todorčević, “Cellularity of covariant functors,” Topology Appl. 76(2), 125–150 (1997).
T. Radul, “On the functor of order-preserving functionals,” Comment. Math. Univ. Carolin. 39(3), 609–615 (1998).
P. S. Aleksandrov and B. A. Pasynkov, An Introduction to the Theory of Topological Spaces and the General Theory of Dimension (Nauka, Moscow, 1973) [in Russian].
V. N. Basmanov, “Covariant functors, retracts, and dimension,” Dokl. Akad. Nauk SSSR 271(5), 1033–1036 (1983).
E. K. van Douwen, “Density of compactifications,” in Set-Theoretic Topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976) (Academic, New York, 1977), pp. 97–110.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R. B. Beshimov, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 4, pp. 527–531.
Rights and permissions
About this article
Cite this article
Beshimov, R.B. Nonincrease of density and weak density under weakly normal functors. Math Notes 84, 493–497 (2008). https://doi.org/10.1134/S0001434608090216
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434608090216