| Title:
|
Countably z-compact spaces (English) |
| Author:
|
Al-Ani, A.T. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
97-100 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions are given. (English) |
| Keyword:
|
z-compact space |
| Keyword:
|
z-Lindelof space |
| Keyword:
|
compact space |
| Keyword:
|
pseudocompact space |
| Keyword:
|
realcompact space |
| MSC:
|
54C60 |
| MSC:
|
54D30 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 06391568 |
| idMR:
|
MR3215282 |
| DOI:
|
10.5817/AM2014-2-97 |
| . |
| Date available:
|
2014-05-23T09:33:09Z |
| Last updated:
|
2015-03-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143782 |
| . |
| Reference:
|
[1] Frolik, Z.: Generalizations of compact and Lindelof spaces.Czechoslovak Math. J. 9 (84) (1959), 172–217, (Russian). Zbl 0098.14201, MR 0105075 |
| Reference:
|
[2] Gillman, L., Jerison, M.: Rings of continuous functions.University Series in Higher Mathematics, Springer-Verlag, 1960. Zbl 0093.30001, MR 0116199 |
| Reference:
|
[3] Kirch, A.M.: A countable, connected, locally connected Hausdorff space.Amer. Math. Monthly 76 (1969), 169–171. Zbl 0174.25602, MR 0239563, 10.2307/2317265 |
| Reference:
|
[4] Kohli, J.K.: Quasi z-supercontinuous and pseudo z-supercontinuous functions.Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău 14 (2004) (2005), 43–56. MR 2239863 |
| Reference:
|
[5] Steen, L.A., Seebach, J. A., Jr., : Counterexamples in Topology.second ed., Springer-Verlag, 1978. Zbl 0386.54001, MR 0507446 |
| . |
