| Title:
|
Čech-completeness and ultracompleteness in “nice spaces” (English) |
| Author:
|
de Luna, Miguel López |
| Author:
|
Tkachuk, Vladimir V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
515-524 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that if $X^n$ is a union of $n$ subspaces of pointwise countable type then the space $X$ is of pointwise countable type. If $X^\omega $ is a countable union of ultracomplete spaces, the space $X^\omega $ is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2]. (English) |
| Keyword:
|
ultracompleteness |
| Keyword:
|
Čech-completeness |
| Keyword:
|
countable type |
| Keyword:
|
pointwise countable type |
| MSC:
|
54C10 |
| MSC:
|
54C25 |
| MSC:
|
54D06 |
| MSC:
|
54D25 |
| MSC:
|
54D35 |
| MSC:
|
54D70 |
| MSC:
|
54E50 |
| MSC:
|
54F65 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1090.54023 |
| idMR:
|
MR1920527 |
| . |
| Date available:
|
2009-01-08T19:24:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119341 |
| . |
| Reference:
|
[Ar] Arhangel'skiĭ A.V.: Bicompact sets and the topology of spaces.Dokl. Akad. Nauk SSSR 150 (1963), 9-12. MR 0150733 |
| Reference:
|
[BY1] Buhagiar D., Yoshioka I.: Ultracomplete topological spaces.preprint. Zbl 1019.54015, MR 1924245 |
| Reference:
|
[BY2] Buhagiar D., Yoshioka I.: Sums and products of ultracomplete topological spaces.Topology Appl., to appear. Zbl 1019.54015, MR 1919293 |
| Reference:
|
[BGT] Balogh Z, Gruenhage G., Tkachuk V.: Additivity of metrizability and related properties.Topology Appl. (1998), 84 91-103. Zbl 0991.54032, MR 1611277 |
| Reference:
|
[Lo] López de Luna M.: Some new results on Čech-complete spaces.Topology Proceedings, vol.24, 1999. MR 1876382 |
| Reference:
|
[Pa] Pasynkov B.A.: Almost metrizable topological groups (in Russian).Dokl. Akad. Nauk SSSR (1965), 161.2 281-284. MR 0204565 |
| Reference:
|
[PT] Ponomarev V.I., Tkachuk V.V.: The countable character of $X$ in $\beta X$ compared with the countable character of the diagonal in $X\times X$.Vestnik Moskovskogo Universiteta, Matematika, 42 (1987), 5 16-19. Zbl 0652.54003, MR 0913263 |
| Reference:
|
[Tk] Tkachuk V.V.: Finite and countable additivity topological properties in nice spaces.Trans. Amer. Math. Soc. (1994), 341 585-601. MR 1129438 |
| Reference:
|
[Tk1] Tkachenko M.G.: On a property of bicompacta.Seminar on General Topology, ed. by P.S. Alexandroff, Mosc. Univ. P.H., Moscow, 1981, pp.149-156. Zbl 0491.54002, MR 0656955 |
| . |
