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Images on locally separable metric spaces. (English) Zbl 0881.54014

For characterizations for certain images of metric spaces, as is well known, some (nice) results on quotient \(s\)-images, or closed images have been obtained by means of certain \(k\)-networks etc., and ones for quotient compact images have been also obtained by means of certain weak bases, etc. In this paper for certain images of locally separable metric spaces (internal) characterizations for those images and some related matters are given.
Reviewer: Y.Tanaka (Tokyo)

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D55 Sequential spaces
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References:

[1] Arhangel’skii A. Mappings and spaces. Russian Math Surveys, 1966, 21 (4): 115–162 · Zbl 0171.43603 · doi:10.1070/RM1966v021n04ABEH004169
[2] Foged L. A characterization of closed images of metric spaces. Proc AMS, 1985, 95: 487–490 · Zbl 0592.54027 · doi:10.1090/S0002-9939-1985-0806093-3
[3] Gruenhage G, Michael E, Tanaka Y. Spaces determined by point-countable covers. Pacific J Math, 1984, 113: 303–332 · Zbl 0561.54016 · doi:10.2140/pjm.1984.113.303
[4] Michael E. A quintuple quotient quest. General Topology Appl, 1972, 2: 91–138 · Zbl 0238.54009 · doi:10.1016/0016-660X(72)90040-2
[5] Tanaka Y. Point-countable covers andk-networks. Topology Proc, 1987, 12: 327–349 · Zbl 0676.54035
[6] Lin Shou. On the quotient compact images of metric spaces. Adv Math (China), 1992, 21: 93–96 · Zbl 0786.54011
[7] Engelking R. General Topology, Warszawa: Polish Scientific Publishers, 1977
[8] Lin Shou. The sequence-coverings-images of metric spaces. Northeastern Math J, 1993, 9: 81–85 · Zbl 0841.54028
[9] Lin Shou. Spaces with a locally countablek-network. Northeastern Math J, 1990, 6:39–44 · Zbl 0704.54017
[10] Liu Chuan. On spaces with locally countablek-networks. J Guangxi University (in Chinese), 1991, 16: 71–74
[11] Tanaka Y. Metrizability of certain quotient spaces. Fund Math, 1983, 119:157–168 · Zbl 0542.54022
[12] Gruenhage G. Generalized metric space. in Kunen K, Vaughan J E Eds, Handbook of Set-Theoretic Topology, Amsterdam: Elsevier Science Publishing Company, 1984, 423–502
[13] Lin Shou. On a problem ofK. Tamano, Questions Answers General Topology, 1988, 6: 99–102 · Zbl 0648.54026
[14] Tanaka Y. Decompositions of spaces determined by compact subsets. Proc AMS, 1986, 97: 549–555 · Zbl 0593.54009 · doi:10.1090/S0002-9939-1986-0840644-9
[15] Lin Shou. A decomposition theorem for -spaces. Topology Proc, 1990, 15: 117–120 · Zbl 0773.54007
[16] Lin Shou. A study of pseudobases. Questions Answers General Topology, 1988, 6: 81–87 · Zbl 0655.54020
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