| Title:
|
Irresolvable countable spaces of weight less than $\frak C$ (English) |
| Author:
|
Malykhin, V. I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
181-185 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct in Bell-Kunen's model: (a) a group maximal topology on a countable infinite Boolean group of weight $\aleph_1 < {\frak C}$ and (b) a countable irresolvable dense subspace of $2^{\omega_1}$. In this model ${\frak C}=\aleph_{\omega_1}$. (English) |
| Keyword:
|
resolvability |
| Keyword:
|
irresolvability |
| Keyword:
|
Martin's Axiom |
| Keyword:
|
a space of weight less than $\frak C$ |
| MSC:
|
20K45 |
| MSC:
|
22A05 |
| MSC:
|
22A30 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54E15 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 1060.54500 |
| idMR:
|
MR1715211 |
| . |
| Date available:
|
2009-01-08T18:50:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119072 |
| . |
| Reference:
|
[E] El'kin A.G.: Resolvable spaces which are not maximally resolvable.Bull. Moscow Univ. Ser. Math. Mech. 24 (1969), 66-70. Zbl 0183.51204, MR 0256331 |
| Reference:
|
[BK] Bell M., Kunen K.: On the $\pi$-character of ultrafilters.C.R. Math. Rep. Acad. Sci. Canada 3 (1981), 351-356. Zbl 0475.54001, MR 0642449 |
| Reference:
|
[He] Hewitt E.: A problem of set-theoretic topology.Duke Math. J. 10 (1943), 309-333. Zbl 0060.39407, MR 0008692 |
| Reference:
|
[K] Kunen K.: Set Theory, The Introduction to Independence Proofs.North Holland Publ. Co. Amsterdam-New York, 1980. MR 0597342 |
| Reference:
|
[Ma] Malykhin V.I.: Extremaly disconnected and nearly extremaly disconnected groups.Soviet Math. Dokl. 16 (1975), 21-25. |
| . |
