# Article

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Keywords:
weak-bases; $cs$-networks; $k$-networks; $g$-first countable spaces; weakly open mappings; msss-mappings.
Summary:
In this paper, spaces with $\sigma$-locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or $g$-first countable spaces with $\sigma$-locally countable $cs$-networks).
References:
[1] Arhangel’skii A.: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162. MR 0227950
[2] Liu C., Dai M.: $g$-metrizability and $S_\omega$. Topology Appl. 60 (1994), 185–189. MR 1302472
[3] Michael E.: $\sigma$-locally finite mappings. Proc. Amer. Math. Soc. 65 (1977), 159–164. MR 0442878
[4] Siwiec F.: On defining a space by a weak-base. Pacific J. Math. 52 (1974), 233–245. MR 0350706 | Zbl 0285.54022
[5] Nagata J.: General metric spaces I. in Topics in General Topology, North-Holland, Amsterdam, 1989. MR 1053200
[6] Foged L.: On $g$-metrizability. Pacific J. Math. 98 (1982), 327–332. MR 0650013 | Zbl 0478.54025
[7] Lin S.: Locally countable families, locally finite families and Alexandroff’s problems. Acta Math. Sinica 37 (1994), 491–496. MR 1337096
[8] Lin S.: Generalized metric spaces and mappings. Chinese Sci. Bull., Beijing, 1995. MR 1375020
[9] Lin S.: On Lašnev spaces. Acta Math. Sinica 34 (1991), 222–225. MR 1117082 | Zbl 0760.54023
[10] Lin S., Tanaka Y.: Point-countable $k$-networks, closed maps, and related results. Topology Appl. 59 (1994), 79–86. MR 1293119 | Zbl 0817.54025
[11] Lin S., Li Z., Li J., Liu C.: On $ss$-mappings. Northeast. Math. J. 9 (1993), 521–524. MR 1274005 | Zbl 0817.54024
[12] Xia S.: Characterizations of certain $g$-first countable spaces. Adv. Math. 29 (2000), 61–64. MR 1769127 | Zbl 0999.54010
[13] Tanaka Y., Xia S.: Certain $s$-images of locally separable metric spaces. Questions Answers Gen. Topology 14 (1996), 217–231. MR 1403347 | Zbl 0858.54030
[14] Tanaka Y., Li Z.: Certain covering-maps and $k$-networks, and related matters. Topology Proc. 27 (2003), 317–334. MR 2048941 | Zbl 1075.54010
[15] Li Z., Lin S.: On the weak-open images of metric spaces. Czechoslovak Math. J. 54 (2004), 393–400. MR 2059259 | Zbl 1080.54509
[16] Li Z.: Spaces with a $\sigma$-locally countable base. Far East J. Math. Sci. 13 (2004), 101–108. MR 2069831 | Zbl 0402.54016

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