| Title:
|
Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces (English) |
| Author:
|
Koldunov, A. V. |
| Author:
|
Veksler, A. I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
363-378 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In [5] the following question was put: are there any maximal n.d. sets in $\omega^*$? Already in [9] the negative answer (under {\bf MA}) to this question was obtained. Moreover, in [9] it was shown that no $P$-set can be maximal n.d. In the present paper the notion of a maximal n.d. $P$-set is introduced and it is proved that under {\bf CH} there is no such a set in $\omega^*$. The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. $P$-sets in basically disconnected compact spaces with rich families of n.d. $P$-sets is actually solved. (English) |
| Keyword:
|
maximal n.d. set |
| Keyword:
|
$P$-set |
| Keyword:
|
maximal n.d. $P$-set |
| Keyword:
|
compact space |
| Keyword:
|
basically disconnected space |
| Keyword:
|
$F$-space |
| MSC:
|
54B05 |
| MSC:
|
54D30 |
| MSC:
|
54D40 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 1053.54041 |
| idMR:
|
MR1832155 |
| . |
| Date available:
|
2009-01-08T19:10:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119251 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
