| Title:
|
A note on $g$-metrizable spaces (English) |
| Author:
|
Li, Jinjin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
491-495 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the relationships between metric spaces and $g$-metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems. (English) |
| Keyword:
|
metric spaces |
| Keyword:
|
$g$-metrizable spaces |
| Keyword:
|
1-sequence-covering mappings |
| Keyword:
|
$\sigma $-mappings |
| Keyword:
|
quotient mappings |
| MSC:
|
54C10 |
| MSC:
|
54D55 |
| MSC:
|
54E35 |
| MSC:
|
54E99 |
| idZBL:
|
Zbl 1026.54026 |
| idMR:
|
MR1983468 |
| . |
| Date available:
|
2009-09-24T11:03:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127816 |
| . |
| Reference:
|
[1] P. Alexandroff: On some results concerning topological spaces and their continuous mappings.In: Proc. Symp. Gen. Top. (Prague, 1961), 1961, pp. 41–54. MR 0145472 |
| Reference:
|
[2] F. Siwiec: On defining a space by a weak base.Pacific J. Math. 52 (1974), 233–245. Zbl 0285.54022, MR 0350706, 10.2140/pjm.1974.52.233 |
| Reference:
|
[3] Shou Lin: On sequence-covering $s$-mappings.Adv. Math. (China) 25 (1996), 548–551. MR 1453163 |
| Reference:
|
[4] Shou Lin: $\sigma $-mappings and Alexandroff’s problems.(to appear). |
| Reference:
|
[5] J. R. Boone and F. Siwiec: Sequentially quotient mappings.Czechoslovak Math. J. 26 (1976), 174–182. MR 0402689 |
| Reference:
|
[6] R. Engelking: General Topology.Polish Scientific Publishers, Warszawa, 1977. Zbl 0373.54002, MR 0500780 |
| Reference:
|
[7] A. V. Arhangel’skii: Mappings and spaces.Russian Math. Surveys 21 (1966), 115–162. MR 0227950 |
| Reference:
|
[8] Y. Tanaka: $\sigma $-hereditarily closure-preserving $k$-networks and $g$-metrizability.Proc. Amer. Math. Soc. 112 (1991), 283–290. Zbl 0770.54031, MR 1049850 |
| . |
