# Article

 Title: Notes on $cfp$-covers (English) Author: Lin, Shou Author: Yan, Pengfei Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 44 Issue: 2 Year: 2003 Pages: 295-306 . Category: math . Summary: The main purpose of this paper is to establish general conditions under which $T_2$-spaces are compact-covering images of metric spaces by using the concept of $cfp$-covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of $g$-metrizable spaces by compact-covering $\sigma$-maps and $mssc$-maps. (English) Keyword: $cfp$-covers Keyword: compact-covering maps Keyword: metrizable spaces Keyword: $g$-metrizable spaces Keyword: $\sigma$-maps Keyword: $mssc$-maps MSC: 54C10 MSC: 54E18 MSC: 54E40 idZBL: Zbl 1100.54021 idMR: MR2026164 . Date available: 2009-01-08T19:29:18Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/119386 . Reference: [1] Arhangel'skiĭ A.V.: Mappings and spaces (in Russian).Uspechi Mat. Nauk 21 (1966), 4 133-184; Russian Math. Surveys 21 (1966), no. 4, 115-162. MR 0227950 Reference: [2] Fleissner W.F., Reed M.G.: Paralindelöf spaces and spaces with a $\sigma$-locally countable base.Topology Proc. 2 (1977), 89-110. MR 0540598 Reference: [3] Foged L.: On $g$-metrizability.Pacific J. Math. 98 (1982), 327-332. Zbl 0478.54025, MR 0650013 Reference: [4] Foged L.: Characterization of $\aleph$-spaces.Pacific J. Math. 110 (1984), 59-63. MR 0722737 Reference: [5] Zhimin Gao: $\aleph$-spaces is invariant under perfect mappings.Questions Answers Gen. Topology 5 (1987), 271-279. MR 0917885 Reference: [6] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers.Pacific J. Math. 113 (1984), 303-332. Zbl 0561.54016, MR 0749538 Reference: [7] Ikeda Y., Chuan Liu, Tanaka Y.: Quotient compact images of metric spaces, and related matters.Topology Appl. 122 (2002), 237-252. MR 1919303 Reference: [8] Shou Lin: $\sigma$-maps and the Alexandroff's problem (in Chinese).Proc. First Academic Annual Meeting of Youth of Fujian Association for Science and Technology, Fuzhou, China, 1992, pp.4-8. MR 1252903 Reference: [9] Shou Lin: Locally countable collections, locally finite collections and Alexandroff's problems (in Chinese).Acta Math. Sinica 37 (1994), 491-496. MR 1337096 Reference: [10] Shou Lin: Generalized Metric Spaces and Mappings (in Chinese).Science Press of China, Beijing, 1995. MR 1375020 Reference: [11] Chuan Liu, Mumin Dai: The compact-covering $s$-images of metric spaces (in Chinese).Acta Math. Sinica 39 (1996), 41-44. MR 1412902 Reference: [12] Michael E.A.: A theorem on semi-continuous set-valued functions.Duke Math. J. 26 (1959), 647-656. Zbl 0151.30805, MR 0109343 Reference: [13] Michael E.A.: $\sigma$-locally finite maps.Proc. Amer. Math. Soc. 65 (1977), 159-164. Zbl 0356.54034, MR 0442878 Reference: [14] Michael E.A., Nagami K.: Compact-covering images of metric spaces.Proc. Amer. Math. Soc. 37 (1973), 260-266. Zbl 0228.54008, MR 0307148 Reference: [15] Siwiec F.: On defining a space by a weak base.Pacific J. Math. 52 (1974), 233-245. Zbl 0285.54022, MR 0350706 Reference: [16] Tanaka Y.: On open finite-to-one maps.Bull. Tokyo Gakugei Univ. Ser. IV 25 (1973), 1-13. Zbl 0355.54008, MR 0346730 Reference: [17] Tanaka Y.: Point-countable covers and $k$-networks.Topology Proc. 12 (1987), 327-349. Zbl 0676.54035, MR 0991759 Reference: [18] Tanaka Y.: Symmetric spaces, $g$-developable spaces and $g$-metrizable spaces.Math. Japonica 36 (1991), 71-84. Zbl 0732.54023, MR 1093356 Reference: [19] Pengfei Yan, Shou Lin: The compact-covering $s$-maps of metric spaces (in Chinese).Acta Math. Sinica 42 (1999), 241-244. MR 1701751 Reference: [20] Pengfei Yan: The compact images of metric spaces (in Chinese).J. Math. Study 30 (1997), 185-187, 198. MR 1468151 .

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