Spaces with $\sigma$-locally countable weak-bases
Li, Zhaowen
Archivum Mathematicum, Tome 042 (2006), p. 135-140 / Harvested from Czech Digital Mathematics Library

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).

Publié le : 2006-01-01
Classification:  54C10,  54E99
@article{107989,
     author = {Zhaowen Li},
     title = {Spaces with $\sigma$-locally countable weak-bases},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {135-140},
     zbl = {1164.54369},
     mrnumber = {2240190},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107989}
}
Li, Zhaowen. Spaces with $\sigma$-locally countable weak-bases. Archivum Mathematicum, Tome 042 (2006) pp. 135-140. http://gdmltest.u-ga.fr/item/107989/

Arhangel’Skii A. Mappings and spaces, Russian Math. Surveys 21 (1966), 115–162. (1966) | MR 0227950

Liu C.; Dai M. $g$-metrizability and $S_\omega $, Topology Appl. 60 (1994), 185–189. (1994) | MR 1302472

Michael E. $\sigma $-locally finite mappings, Proc. Amer. Math. Soc. 65 (1977), 159–164. (1977) | MR 0442878

Siwiec F. On defining a space by a weak-base, Pacific J. Math. 52 (1974), 233–245. (1974) | MR 0350706 | Zbl 0285.54022

Nagata J. General metric spaces I, in Topics in General Topology, North-Holland, Amsterdam, 1989. (1989) | MR 1053200

Foged L. On $g$-metrizability, Pacific J. Math. 98 (1982), 327–332. (1982) | MR 0650013 | Zbl 0478.54025

Lin S. Locally countable families, locally finite families and Alexandroff’s problems, Acta Math. Sinica 37 (1994), 491–496. (1994) | MR 1337096

Lin S. Generalized metric spaces and mappings, Chinese Sci. Bull., Beijing, 1995. (1995) | MR 1375020

Lin S. On Lašnev spaces, Acta Math. Sinica 34 (1991), 222–225. (1991) | MR 1117082 | Zbl 0760.54023

Lin S.; Tanaka Y. Point-countable $k$-networks, closed maps, and related results, Topology Appl. 59 (1994), 79–86. (1994) | MR 1293119 | Zbl 0817.54025

Lin S.; Li Z.; Li J.; Liu C. On $ss$-mappings, Northeast. Math. J. 9 (1993), 521–524. (1993) | MR 1274005 | Zbl 0817.54024

Xia S. Characterizations of certain $g$-first countable spaces, Adv. Math. 29 (2000), 61–64. | MR 1769127 | Zbl 0999.54010

Tanaka Y.; Xia S. Certain $s$-images of locally separable metric spaces, Questions Answers Gen. Topology 14 (1996), 217–231. (1996) | MR 1403347 | Zbl 0858.54030

Tanaka Y.; Li Z. Certain covering-maps and $k$-networks, and related matters, Topology Proc. 27 (2003), 317–334. | MR 2048941 | Zbl 1075.54010

Li Z.; Lin S. On the weak-open images of metric spaces, Czechoslovak Math. J. 54 (2004), 393–400. | MR 2059259 | Zbl 1080.54509

Li Z. Spaces with a $\sigma $-locally countable base, Far East J. Math. Sci. 13 (2004), 101–108. | MR 2069831 | Zbl 0402.54016