| Title:
|
On powers of Lindelöf spaces (English) |
| Author:
|
Gorelic, Isaac |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
383-401 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space $X$ whose square $X^2$ is again Lindelöf but its cube $X^3$ has a closed discrete subspace of size ${\frak c}^+$, hence the Lindelöf degree $L(X^3) = {\frak c}^+ $. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space $X$ such that $L(X^n) = \aleph_0$ for all positive integers $n$, but $L(X^{\aleph_0}) = {\frak c}^+ = \aleph_2$. (English) |
| Keyword:
|
forcing |
| Keyword:
|
topology |
| Keyword:
|
products |
| Keyword:
|
Lindelöf |
| MSC:
|
03E35 |
| MSC:
|
54A35 |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 0815.54015 |
| idMR:
|
MR1286586 |
| . |
| Date available:
|
2009-01-08T18:11:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118678 |
| . |
| Reference:
|
[1] Shelah S.: On some problems in general topology.preprint, 1978. Zbl 0847.54004, MR 1367138 |
| Reference:
|
[2] Juhász I.: Cardinal Functions II.in: K. Kunen and J.E. Vaughan, eds., Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984. MR 0776621 |
| Reference:
|
[3] Hajnal A., Juhàsz I.: Lindelöf spaces à la Shelah.Coll. Mat. Soc. Bolyai, Budapest, 1978. |
| Reference:
|
[4] Gorelic I.: The Baire Category and forcing large Lindelöf spaces with points $G_\delta$.Proceedings Amer. Math. Soc. 118 (1993), 603-607. MR 1132417 |
| Reference:
|
[5] Juhász I.: Cardinal Functions.in: M. Hušek and J. van Mill, eds., Recent Progress in General Topology, North-Holland, 1992. MR 1229134 |
| Reference:
|
[6] Przymusinski T.C.: Normality and paracompactness in finite and countable cartesian products.Fund. Math. 105 (1980), 87-104. Zbl 0438.54021, MR 0561584 |
| Reference:
|
[7] Kunen K.: Set Theory.North-Holland, Amsterdam, 1980. Zbl 0960.03033, MR 0597342 |
| . |
