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New properties of topological spaces generalizing extreme non-connectivity
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 19-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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New classes $R_1$, $R_2$, $R_3$ of topological spaces generalizing the class of $F$-spaces are introduced. It is proved that all homogeneous compact subspaces of spaces in these classes and of some of their products are finite. Results on the Rudin–Keisler comparability of ultrafilters along which distinct sequences converge to the same point in $R_2$- and $R_3$-spaces are obtained. 
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A. Yu. Groznova; O. V. Sipacheva. New properties of topological spaces generalizing extreme non-connectivity. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 19-25. http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a2/

[1] Gleason A.M., “Projective topological spaces”, Ill. J. Math., 2:4A (1958), 482–489

[2] Ponomarev V.I., “Ob absolyute topologicheskogo prostranstva”, Dokl. AN SSSR, 149 (1963), 26–29

[3] Johnstone P.T., Stone Spaces, Cambridge Univ. Press, Cambridge, 1982

[4] Gillman L., Jerison M., Rings of Continuous Functions, Springer, N.Y., 1960

[5] Van Douwen E.K., Prime Mappings, Number of Factors and Binary Operations, Dissertationes Math., 199, PWN, Warszawa, 1981

[6] Comfort W.W., “Ultrafiters: some old and some new results”, Bull. Amer. Math. Soc., 83 (1977), 417–455

[7] Husek M., “Continuous mappings on subspaces of products”, Symp. Math., 17 (1976), 25–41

[8] Kunen K., “Weak $P$-points in $N^*$”, Colloq. Math. Soc. János Bolyai, 23, 1978, 741–749

[9] Frolik Z., “Maps of extremally disconnected spaces, theory of types, and applications”, General Topology and Its Relations to Modern Analysis and Algebra, Proc. Kanpur Topological Conf. (1968), Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971, 133–142

[10] Reznichenko E., “Homogeneous subspaces of products of extremally disconnected spaces”, Topol. and Appl., 284 (2020), 107403

[11] Engelking R., Obschaya topologiya, Mir, M., 1986

[12] Verner J.L., “Lonely points revisited”, Comment. Math. Univ. Carolin., 54 (2013), 105–110

[13] Levy R., “Semi-F-spaces”, Bull. Canad. Math., 31 (1988), 385–393

[14] Comfort W.W., Negrepontis S., The Theory of Ultrafilters, Springer-Verlag, Berlin, 1974

[15] Frolík Z., “Sums of ultrafilters”, Bull. Amer. Math. Soc., 73 (1967), 87–91

[16] Kunen K., “Large homogeneous compact spaces”, Open Problems in Topology, North-Holland, Amsterdam, 1990, 262–270