| Title:
|
$k$-systems, $k$-networks and $k$-covers (English) |
| Author:
|
Li, Jinjin |
| Author:
|
Lin, Shou |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
239-245 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concepts of $k$-systems, $k$-networks and $k$-covers were defined by A. Arhangel’skiǐ in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among $k$-systems, $k$-networks and $k$-covers are further discussed and are established by $mk$-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of $mk$-systems. (English) |
| Keyword:
|
$k$-systems |
| Keyword:
|
$k$-networks |
| Keyword:
|
$k$-covers |
| Keyword:
|
$k$-spaces |
| Keyword:
|
point-countable families |
| Keyword:
|
hereditarily closure-preserving families |
| MSC:
|
54C10 |
| MSC:
|
54D50 |
| MSC:
|
54E45 |
| idZBL:
|
Zbl 1164.54359 |
| idMR:
|
MR2207015 |
| . |
| Date available:
|
2009-09-24T11:32:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128062 |
| . |
| Reference:
|
[1] A. Arhangel’skiǐ: On quotient mappings of metric spaces.Dokl. Akad. Nauk. SSSR 155 (1964), 247–250. (Russian) |
| Reference:
|
[2] D. K. Burke: ARRAY(0x9a06458).K. Kunen, J. E. Vaughan (eds.), North-Holland, , 1984, pp. 347–422. MR 0776619 |
| Reference:
|
[3] J. Chaber: Generalizations of Lašnev’s theorem.Fund. Math. 119 (1983), 85–91. Zbl 0547.54009, MR 0731811, 10.4064/fm-119-2-85-91 |
| Reference:
|
[4] Huaipeng Chen: On $s$-images of metric spaces.Topology Proc. 24 (1999), 95–103. MR 1802679 |
| Reference:
|
[5] L. Foged: A characterization of closed images of metric spaces.Proc. Amer. Math. Soc. 95 (1985), 487–490. Zbl 0592.54027, MR 0806093, 10.1090/S0002-9939-1985-0806093-3 |
| Reference:
|
[6] G. Gruenhage: Generalized metric spaces.In: Handbook of Set-theoretic Topology, K. Kunen, J. E. Vaughan (eds.), North-Holland, , 1984, pp. 423–501. Zbl 0555.54015, MR 0776629 |
| Reference:
|
[7] G. Gruenhage, E. Michael, and Y. Tanaka: Spaces determined by point-countable covers.Pacific J. Math. 113 (1984), 303–332. MR 0749538, 10.2140/pjm.1984.113.303 |
| Reference:
|
[8] Jinjin Li: $k$-covers and certain quotient images of paracompact locally compact spaces.Acta Math. Hungar. 95 (2002), 281–286. MR 1909598, 10.1023/A:1015645107703 |
| Reference:
|
[9] Jinjin Li, Shou Lin: Spaces with compact-countable $k$-systems.Acta Math. Hungar. 93 (2001), 1–6. MR 1924664, 10.1023/A:1013807430701 |
| Reference:
|
[10] Zhaowen Li, Jinjin Li: On Michael-Nagami’s problem.Questions Answers in General Topology 12 (1994), 85–91. |
| Reference:
|
[11] Shou Lin: On spaces with a $k$-network consisting of compact subsets.Topology Proc. 20 (1995), 185–190. MR 1429180 |
| Reference:
|
[12] R. A. McCoy, I. Ntantu: Countability properties of function spaces with set-open topologies.Topology Proc. 10 (1985), 329–345. MR 0876902 |
| Reference:
|
[13] E. Michael: A note on closed maps and compact sets.Israel J. Math. 2 (1964), 173–176. Zbl 0136.19303, MR 0177396, 10.1007/BF02759940 |
| Reference:
|
[14] P. O’Meara: On paracompactness in function spaces with the compact-open topology.Proc. Amer. Math. Soc. 29 (1971), 183–189. MR 0276919, 10.1090/S0002-9939-1971-0276919-3 |
| Reference:
|
[15] M. Sakai: On spaces with a point-countable compact $k$-network.Yokohama Math. J. 48 (2000), 13–16. Zbl 0964.54023, MR 1788830 |
| Reference:
|
[16] Y. Tanaka: Closed images of locally compact spaces and Fréchet space.Topology Proc. 7 (1982), 279–292. MR 0715799 |
| Reference:
|
[17] Y. Tanaka: Point-countable $k$-systems and products of $k$-spaces.Pacific J. Math. 101 (1982), 199–208. Zbl 0498.54023, MR 0671852, 10.2140/pjm.1982.101.199 |
| Reference:
|
[18] Y. Tanaka: Theory of $k$-networks II.Questions Answers in General Topology 19 (2001), 27–46. Zbl 0970.54023, MR 1815344 |
| . |
