| Title:
|
Closed subsets of absolutely star-Lindelöf spaces II (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
329-334 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed $G_{\delta}$ subspace. (English) |
| Keyword:
|
star-Lindelöf space |
| Keyword:
|
absolutely star-Lindelöf space |
| MSC:
|
54B05 |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54D35 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1100.54017 |
| idMR:
|
MR2026167 |
| . |
| Date available:
|
2009-01-08T19:29:33Z |
| Last updated:
|
2020-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119389 |
| . |
| Reference:
|
[1] Bonanzinga M.: Star-Lindelöf and absolutely star-Lindelöf spaces.Questions Answers Gen. Topology 16 (1998), 79-104. Zbl 0931.54019, MR 1642032 |
| Reference:
|
[2] Bonanzinga M., Matveev M.V.: Closed subspaces of star-Lindelöf and related spaces.to appear in East-West J. Math. Zbl 0997.54035, MR 1825453 |
| Reference:
|
[3] Bonanzinga M., Matveev M.V.: Products of star-Lindelöf and related spaces.Houston J. Math. 27 (2001), 45-57. Zbl 0983.54006, MR 1843911 |
| Reference:
|
[4] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J.: Star covering properties.Topology Appl. 39 (1991), 71-103. Zbl 0743.54007, MR 1103993, 10.1016/0166-8641(91)90077-Y |
| Reference:
|
[5] Engelking R.: General Topology, Revised and completed edition.Heldermann Verlag Berlin (1989). MR 1039321 |
| Reference:
|
[6] Matveev M.V.: Absolutely countably compact spaces.Topology Appl. 58 (1994), 81-92. Zbl 0801.54021, MR 1280711, 10.1016/0166-8641(94)90074-4 |
| Reference:
|
[7] Matveev M.V.: A survey on star-covering properties.Topology Atlas preprint No. 330 (1998). |
| Reference:
|
[8] Song Y.-K.: Remarks on star-Lindelöf spaces.Questions Answers Gen. Topology 20 (2002), 49-51. Zbl 1006.54032, MR 1910431 |
| Reference:
|
[9] Song Y.-K., Shi W.-X.: Closed subspaces of absolutely star-Lindelöf spaces.to appear in Houston J. Math. MR 2084912 |
| Reference:
|
[10] Vaughan J.E.: On the product of a compact space with an absolutely countably compact space.Annals of the New York Acad. Sci. 788 (1996), 203-208. Zbl 0917.54023, MR 1460834, 10.1111/j.1749-6632.1996.tb36814.x |
| Reference:
|
[11] Vaughan J.E.: Absolute countable compactness and property $(a)$.Talk at 1996 Praha symposium on General Topology. |
| . |
