| Title:
|
A countably compact, separable space which is not absolutely countably compact (English) |
| Author:
|
Vaughan, Jerry E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
197-201 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a space having the properties in the title, and with the same technique, a countably compact $T_2$ topological group which is not absolutely countably compact. (English) |
| Keyword:
|
countably compact |
| Keyword:
|
absolutely countably compact |
| Keyword:
|
topological group |
| Keyword:
|
Franklin-Rajagopalan space |
| MSC:
|
22A05 |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54G20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0833.54012 |
| idMR:
|
MR1334426 |
| . |
| Date available:
|
2009-01-08T18:16:57Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118744 |
| . |
| Reference:
|
[1] van Douwen E.K.: The integers and topology.in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, eds., North-Holland, Amsterdam, 1984. Zbl 0561.54004, MR 0776622 |
| Reference:
|
[2] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J.: Star covering properties.Topology and Appl. 39 (1991), 71-103. Zbl 0743.54007, MR 1103993 |
| Reference:
|
[3] Engelking R.: General Topology.PWN-Polish Scientific Publications, Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[4] Fleishman W.M.: A new extension of countable compactness.Fund. Math. 67 (1970), 1-9. MR 0264608 |
| Reference:
|
[5] Matveev M.V.: Absolutely countably compact spaces.Topology and Appl. 58 (1994), 81-92. Zbl 0801.54021, MR 1280711 |
| Reference:
|
[6] Matveev M.V.: A countably compact topological group which is not absolutely countably compact.Questions and Answers in General Topology 11 (1993), 173-176. Zbl 0808.54025, MR 1234212 |
| Reference:
|
[7] Noble N.: The continuity of functions on Cartesian products.Trans. Amer. Math. Soc. 149 (1970), 187-198. Zbl 0229.54028, MR 0257987 |
| Reference:
|
[8] Nyikos P.J., Vaughan J.E.: Sequentially compact, Franklin-Rajagopalan spaces.Proc. Amer. Math. Soc. 101 (1987), 149-155. Zbl 0626.54004, MR 0897087 |
| Reference:
|
[9] Scarborough C.T., Stone A.H.: Products of nearly compact spaces.Trans. Amer. Math. Soc. 124 (1966), 131-147. Zbl 0151.30001, MR 0203679 |
| Reference:
|
[10] Vaughan J.E.: Countably compact and sequentially compact spaces.in Handbook of Set- theoretic Topology, eds. K. Kunen and J. Vaughan, North-Holland, Amsterdam, 1984. Zbl 0562.54031, MR 0776631 |
| Reference:
|
[11] Vaughan J.E.: Small uncountable cardinals in topology.in Problems in Topology, eds. Jan van Mill and M.G. Reed, North-Holland, Amsterdam, 1990. MR 1078647 |
| Reference:
|
[12] Vaughan J.E.: A countably compact, separable space which is not absolutely countably compact. Preliminary Report.Abstracts Amer. Math. Soc. 14 (November 1993), No. 888-54-37. |
| . |
