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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:
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..


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