Geodesic
Nonincrease of Density and Weak Density under Weakly Normal Functors
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 527-531.

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In this paper, it is proved that if a covariant functor $\mathscr F\colon\mathrm{Comp}\to\mathrm{Comp}$ is weakly normal, then $d(\mathscr F^\beta(X))\le d(X)$ and $wd(\mathscr F^\beta(X))\le wd(X)$ for any infinite Tychonoff space $X$.
Keywords: normal functor, weakly normal functor, density, weak density, cellularity of a space, Tychonoff space, Stone–Čech compactification.
Mots-clés : Hausdorff space 
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R. B. Beshimov. Nonincrease of Density and Weak Density under Weakly Normal Functors. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 527-531. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a4/

[1] E. V. Schepin, “Funktory i neschetnye stepeni kompaktov”, UMN, 36:3 (1981), 3–62 | MR | Zbl

[2] M. M. Zarichnyi, “O svoistvakh normalnykh funktorov”, Tezisy dokladov V Tiraspolskogo simpoziuma po obschei topologii i ee prilozheniyam, Shtintsa, Kishinev, 1985, 96–97

[3] A. Ch. Chigogidze, “O prodolzhenii normalnykh funktorov”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1984, no. 6, 23–26 | MR | Zbl

[4] A. V. Arkhangelskii, V. I. Ponomarev, Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974 | MR | Zbl

[5] R. B. Beshimov, “Some cardinal properties of topological spaces connected with weakly density”, Methods Funct. Anal. Topology, 10:3 (2004), 17–22 | MR | Zbl

[6] R. B. Beshimov, “A note on weakly separable spaces”, Math. Morav., 6 (2002), 9–19 | MR

[7] B. B. Fedorchuk, V. V. Filippov, Obschaya topologiya. Osnovnye konstruktsii, MGU, M., 1988 | Zbl

[8] V. V. Fedorchuk, S. Todorčević, “Cellularity of covariant functors”, Topology Appl., 76:2 (1997), 125–150 | DOI | MR | Zbl

[9] T. Radul, “On the functor of order-preserving functionals”, Comment. Math. Univ. Carolin., 39:3 (1998), 609–615 | MR | Zbl

[10] P. S. Aleksandrov, B. A. Pasynkov, Vvedenie v teoriyu razmernosti, Hauka, M., 1973 | MR | Zbl

[11] V. N. Basmanov, “Kovariantnye funktory, retrakty i razmernost”, Dokl. AN SSSR, 271:5 (1983), 1033–1036 | MR | Zbl

[12] E. K. van Douwen, “Density of compactifications”, Set-Theoretic Topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976), Academic Press, New York, 1977, 97–110 | MR | Zbl