Regular covers and metrization

• Autorzy: Lin S.
• Języki publikacji: EN

Abstrakty

EN

In this paper it is showed that a regular and k-space with a regular k-network is metrizable, which generalized related results of A. Archangielskiĭ, H. W. Martin, M. Sakai, K. Tamano and Y. Yajima.

Słowa kluczowe

EN

cs*-network; Fréchet space; k-network; k-space; metrizable space; regular cover

PL

cs*-sieć; k-przestrzeń; k-sieć; pokrycie regularne; przestrzeń Frécheta; przestrzeń metryzowalna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 4
• Strony: 427--432
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Lin S.

• Department of Mathematics, Fujian Normal University, Fuzhou 350007, People’s Republic of China

Bibliografia

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• [2] R. Arens, Note on convergence in topology, Math. Mag., 23 (1950) 229-234.
• [3] A. Archangielskiĭ, On the metrization of topological spaces (in Russian), Bull. Acad. Polon. Sci., Sér. sci. math., astr, et phys., 8 (1960) 589-595.
• [4] A. Archangielskiĭ, Mappings and spaces, Uspekhi Mat. Nauk., 21 (4) (1966) 133-184; Russian Math. Surveys, 21 (4) (1966) 115-162.
• [5] S. P. Franklin, Spaces in which sequences suffice, Fund. Math., 57 (1965) 107-115.
• [6] Zhimin Gao, ℵ-space is invariant under perfect mappings, Questions Answers in Gen. Topology, 5 (1987) 271-279.
• [7] G. Gruenhage, E. Michael, Y. Tanaka, Spaces determined by point-countable covers, Pacific J. Math., 113 (1984) 303-332.
• [8] H. Junnila, Y. Yajima, Normality and countable paracompactness of products with σ-spaces having special nets, Topology Appl., 85 (1998) 375-394.
• [9] H. W. Martin, Weak bases and metrization, Trans. Amer. Math. Soc., 222 (1976) 337-344.
• [10] P. O’Meara, On paracompactness in function spaces with the compact open topology, Proc. Amer. Math. Soc., 29 (1971) 183-189.
• [11] M. Sakai, K. Tamano, Y. Yajima, Regular networks for metrizable spaces and Lašnev spaces, Bull. Pol. Ac.: Math., 46 (1998) 121-133.