| Title:
|
Absolute countable compactness of products and topological groups (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
367-372 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)]. (English) |
| Keyword:
|
compact |
| Keyword:
|
countably compact |
| Keyword:
|
absolutely countably compact |
| Keyword:
|
hereditarily absolutely countably compact |
| Keyword:
|
topological group |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54D55 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0976.54021 |
| idMR:
|
MR1732658 |
| . |
| Date available:
|
2009-01-08T18:53:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119093 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: On bicompacta hereditarily satisfying Suslin's condition tightness and free sequences.Soviet Math. Dokl. 12 (1971), 1253-1257. MR 0119188 |
| Reference:
|
[2] Bonanzinga M.: On the product of a compact space with an hereditarily absolutely countably compact space.Comment. Math. Univ. Carolinae 38 (1997), 557-562. Zbl 0937.54013, MR 1485076 |
| Reference:
|
[3] van Douwen E.K.: The Integer and Topology.Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 111-167. MR 0776619 |
| Reference:
|
[4] Engelking R.: General Topology, Revised and completed edition.Heldermann Verlag Berlin (1989). MR 1039321 |
| Reference:
|
[5] Fleishman W.M.: A new extension of countable compactness.Fund. Math. 67 (1970), 1-9. MR 0264608 |
| Reference:
|
[6] Kombarov A.P.: On the product of normal spaces.Soviet. Math. Dokl. 13 (4) (1972), 1068-1071. Zbl 0259.54006 |
| Reference:
|
[7] Matveev M.V.: Absolutely countably compact spaces.Topology Appl. 58 (1994), 81-92. Zbl 0801.54021, MR 1280711 |
| Reference:
|
[8] Matveev M.V.: A countably compact topological group which is not absolutely countably compact.Questions Answers Gen. Topology 11 (1993), 173-176. Zbl 0808.54025, MR 1234212 |
| Reference:
|
[9] Stephenson R.M., Jr.: Initially $\kappa$-Compact and Related Space.Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 603-632. MR 0776632 |
| Reference:
|
[10] Vaughan J.E.: A countably compact, separable space which is not absolutely countably compact.Comment. Math. Univ. Carolinae 34 (1995), 197-200. Zbl 0833.54012, MR 1334426 |
| Reference:
|
[11] Vaughan J.E.: On the product of a compact space with an absolutely countably compact space.Annals of New York Acad. Soc. 788 (1996), 203-208. Zbl 0917.54023, MR 1460834 |
| Reference:
|
[12] Vaughan J.E.: Countably Compact and Sequentially Compact Spaces.Handbook of Set-theoertic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 569-602. Zbl 0562.54031, MR 0776631 |
| . |
