| Title:
|
More than a 0-point (English) |
| Author:
|
Flašková, Jana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
617-621 |
| . |
| Category:
|
math |
| . |
| Summary:
|
\font\tenscr = rsfs10 \font\sevenscr = rsfs7 \font\fivescr = rsfs5 \textfont14=\tenscr \scriptfont14=\sevenscr \scriptscriptfont14=\fivescr \def\scr{\fam14} We construct in ZFC an ultrafilter $\scr U \in \Bbb N^{\ast}$ such that for every one-to-one function $f : \Bbb N\rightarrow \Bbb N$ there exists $U\in \scr U$ with $f[U]$ in the summable ideal, i.e. the sum of reciprocals of its elements converges. This strengthens Gryzlov's result concerning the existence of $0$-points. (English) |
| Keyword:
|
ultrafilter |
| Keyword:
|
$0$-point |
| Keyword:
|
summable ideal |
| Keyword:
|
linked family |
| MSC:
|
54D40 |
| MSC:
|
54G99 |
| idZBL:
|
Zbl 1150.54025 |
| idMR:
|
MR2337416 |
| . |
| Date available:
|
2009-05-05T17:00:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119622 |
| . |
| Reference:
|
[1] Flašková J.: Ultrafilters and two ideals on $ømega $.in: WDS'05 Proceedings of Contributed Papers: Part I - Mathematics and Computer Sciences (ed. Jana Šafránková), Prague, Matfyzpress, 2005, pp.78-83. |
| Reference:
|
[2] Gryzlov A.: Some types of points in $N^{*}$.in: Proceedings of the 12th Winter School on Abstract Analysis (Srní, 1984), Rend. Circ. Mat. Palermo (2) Suppl. No. 6, 1984, pp.137-138. Zbl 0566.54011, MR 0782711 |
| Reference:
|
[3] Gryzlov A.A.: On theory of the space $\beta \Bbb N$.General Topology (Russian), 166, Moskov. Gos. Univ., Moscow, 1986, pp.20-34. MR 1080755 |
| Reference:
|
[4] Hart K.P.: Notes taken at Winter School 1984, Srní, handwritten notes.. |
| . |
