Notes on $cfp$-covers
Lin, Shou ; Yan, Peng Fei
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 295-306 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2003-01-01
Classification:  54C10,  54E18,  54E40 
@article{119386,
     author = {Shou Lin and Peng Fei Yan},
     title = {Notes on $cfp$-covers},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {295-306},
     zbl = {1100.54021},
     mrnumber = {2026164},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119386}
}

Lin, Shou; Yan, Peng Fei. Notes on $cfp$-covers. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 295-306. http://gdmltest.u-ga.fr/item/119386/

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. (1966) | MR 0227950

Fleissner W.F.; Reed M.G. Paralindelöf spaces and spaces with a $\sigma$-locally countable base, Topology Proc. 2 (1977), 89-110. (1977) | MR 0540598

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

Foged L. Characterization of $\aleph$-spaces, Pacific J. Math. 110 (1984), 59-63. (1984) | MR 0722737

Zhimin Gao $\aleph$-spaces is invariant under perfect mappings, Questions Answers Gen. Topology 5 (1987), 271-279. (1987) | MR 0917885

Gruenhage G.; Michael E.; Tanaka Y. Spaces determined by point-countable covers, Pacific J. Math. 113 (1984), 303-332. (1984) | MR 0749538 | Zbl 0561.54016

Ikeda Y.; Chuan Liu; Tanaka Y. Quotient compact images of metric spaces, and related matters, Topology Appl. 122 (2002), 237-252. (2002) | MR 1919303

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

Shou Lin Locally countable collections, locally finite collections and Alexandroff's problems (in Chinese), Acta Math. Sinica 37 (1994), 491-496. (1994) | MR 1337096

Shou Lin Generalized Metric Spaces and Mappings (in Chinese), Science Press of China, Beijing, 1995. | MR 1375020

Chuan Liu; Mumin Dai The compact-covering $s$-images of metric spaces (in Chinese), Acta Math. Sinica 39 (1996), 41-44. (1996) | MR 1412902

Michael E.A. A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-656. (1959) | MR 0109343 | Zbl 0151.30805

Michael E.A. $\sigma$-locally finite maps, Proc. Amer. Math. Soc. 65 (1977), 159-164. (1977) | MR 0442878 | Zbl 0356.54034

Michael E.A.; Nagami K. Compact-covering images of metric spaces, Proc. Amer. Math. Soc. 37 (1973), 260-266. (1973) | MR 0307148 | Zbl 0228.54008

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

Tanaka Y. On open finite-to-one maps, Bull. Tokyo Gakugei Univ. Ser. IV 25 (1973), 1-13. (1973) | MR 0346730 | Zbl 0355.54008

Tanaka Y. Point-countable covers and $k$-networks, Topology Proc. 12 (1987), 327-349. (1987) | MR 0991759 | Zbl 0676.54035

Tanaka Y. Symmetric spaces, $g$-developable spaces and $g$-metrizable spaces, Math. Japonica 36 (1991), 71-84. (1991) | MR 1093356 | Zbl 0732.54023

Pengfei Yan; Shou Lin The compact-covering $s$-maps of metric spaces (in Chinese), Acta Math. Sinica 42 (1999), 241-244. (1999) | MR 1701751

Pengfei Yan The compact images of metric spaces (in Chinese), J. Math. Study 30 (1997), 185-187, 198. (1997) | MR 1468151