| Title:
|
On $k$-spaces and $k_R$-spaces (English) |
| Author:
|
Li, Jinjin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
941-945 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we study the relation between $k_R$-spaces and $k$-spaces and prove that a $k_R$-space with a $\sigma $-hereditarily closure-preserving $k$-network consisting of compact subsets is a $k$-space, and that a $k_R$-space with a point-countable $k$-network consisting of compact subsets need not be a $k$-space. (English) |
| Keyword:
|
$k_R$-spaces |
| Keyword:
|
$k$-spaces |
| Keyword:
|
$k$-networks |
| Keyword:
|
$\sigma $-hereditarily closure-preserving collections |
| Keyword:
|
point-countable collections |
| MSC:
|
54C30 |
| MSC:
|
54D50 |
| idZBL:
|
Zbl 1081.54021 |
| idMR:
|
MR2184375 |
| . |
| Date available:
|
2009-09-24T11:29:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128036 |
| . |
| Reference:
|
[1] V. Pták: On complete topological linear spaces.Czechoslovak Math. J. 3(78) (1953), 301–364. (Russian, English Summary) MR 0064303 |
| Reference:
|
[2] E. Michael: On $k$-spaces, $k_R$-spaces and $k(X)$.Pac. J. Math. 47 (1973), 487–498. Zbl 0262.54017, MR 0331328 |
| Reference:
|
[3] S. Lin: Note on $k_R$-space.Quest. Answers Gen. Topology 9 (1991), 227–236. MR 1113875 |
| Reference:
|
[4] S. Lin: On $R$-quotient $ss$-mappings.Acta Math. Sin. 34 (1991), 7–11. (Chinese) Zbl 0760.54009, MR 1107584 |
| Reference:
|
[5] Z. Yun: On $k_R$-spaces and $k$-spaces.Adv. Math., Beijing 29 (2000), 223–226. Zbl 0996.54037, MR 1789423 |
| Reference:
|
[6] P. O’Meara: On paracompactness in function spaces with the compact-open topology.Proc. Am. Math. Soc. 29 (1971), 183–189. MR 0276919 |
| Reference:
|
[7] 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:
|
[8] R. Borges: A stratifiable $k_R$-space which is not a $k$-space.Proc. Am. Math. Soc. 81 (1981), 308–310. Zbl 0447.54033, MR 0593478 |
| . |
