| Title:
|
Lonely points revisited (English) |
| Author:
|
Verner, Jonathan L. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
105-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point $p\in X$ is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space ${\mathcal G}_\omega$ from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745--748] to construct lonely points in $\omega^*$. This answers the question of P. Simon posed in our paper Lonely points in $\omega^*$, Topology Appl. 155 (2008), no. 16, 1766--1771. (English) |
| Keyword:
|
$\beta\omega$ |
| Keyword:
|
lonely point |
| Keyword:
|
weak P-point |
| Keyword:
|
irresolvable spaces |
| MSC:
|
54D40 |
| MSC:
|
54D80 |
| MSC:
|
54G05 |
| idMR:
|
MR3038075 |
| . |
| Date available:
|
2013-02-21T14:08:55Z |
| Last updated:
|
2015-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143156 |
| . |
| 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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| . |
