Previous |  Up |  Next

Article

Title: Permitted trigonometric thin sets and infinite combinatorics (English)
Author: Repický, Miroslav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 42
Issue: 4
Year: 2001
Pages: 609-627
.
Category: math
.
Summary: We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions. (English)
Keyword: permitted trigonometric thin sets
Keyword: set of perfect measure zero
Keyword: set of uniform measure zero
Keyword: s-set
MSC: 03E05
MSC: 03E17
MSC: 03E50
MSC: 42A24
idZBL: Zbl 1069.03034
idMR: MR1883370
.
Date available: 2009-01-08T19:16:50Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119277
.
Reference: [1] Arbault M.J.: Sur l'ensemble de convergence absolue d'une série trigonométrique.Bull. Soc. Math. France 80 (1952), 253-317. Zbl 0048.04202, MR 0055476
Reference: [2] Bartoszyński T., Recław I.: Not every $\gamma$-set is strongly meager.Set theory (Bartoszynski T. et al., eds.). Annual Boise extravaganza in set theory conference, 1992/1994, Boise State University, Boise, ID, USA Contemp. Math. 192 (1996), 25-29. MR 1367132
Reference: [3] Bartoszyński T., Scheepers M.: Remarks on sets related to trigonometric series.Topology Appl. 64 (1995), 133-140. MR 1340865
Reference: [4] Bary N.K.: azbuka Trigonometricheskie ryady.Moskva (1961), English translation A Treatise on Trigonometric Series Macmillan New York (1964). MR 0171116
Reference: [5] Bukovská Z.: Thin sets in trigonometrical series and quasinormal convergence.Math. Slovaca 40 (1990), 53-62. MR 1094972
Reference: [6] Bukovská Z.: Thin sets defined by a sequence of continuous functions.Math. Slovaca 49 (1999), 3 323-344. MR 1728243
Reference: [7] Bukovská Z., Bukovský L.: Adding small sets to an N-set.Proc. Amer. Math. Soc. 123 (1995), 1367-1373. MR 1285977
Reference: [8] Bukovský L.: Thin sets in a general setting.Tatra Mountains Mathematical Publications 14 (1998), 241-260. MR 1651217
Reference: [9] Bukovský L., Kholshchevnikova N.N., Repický M.: Thin sets of harmonic analysis and infinite combinatorics.Real Anal. Exchange 20 (1994/95), 454-509. MR 1348075
Reference: [10] Bukovský L., Recław I., Repický M.: Spaces not distinguishing convergence of real-valued functions.Topology Appl. 112 (2001), 13-40.
Reference: [11] Galvin F., Miller A.W.: $\gamma$-sets and other singular sets of real numbers.Topology Appl. 17 (1984), 145-155. Zbl 0551.54001, MR 0738943
Reference: [12] Just W., Miller A.W., Scheepers M., Szeptycki P.J.: The combinatorics of open covers, II.Topology Appl. 73 (1996), 3 241-266. Zbl 0870.03021, MR 1419798
Reference: [13] Kada M., Kamo S.: New cardinal invariants related to pseudo-Dirichlet sets.preprint, 1996.
Reference: [14] Kahane S.: Antistable classes of thin sets in harmonic analysis.Illinois J. Math. 37 (1993), 2 186-223. Zbl 0793.42003, MR 1208819
Reference: [15] Kholshchevnikova N.N.: Uncountable R- and N-sets.Math. Notes 38 (1985), 847-851. MR 0808896
Reference: [16] Kholshchevnikova N.N.: azbuka Primenenie teoretiko-mnozhestvennykh metodov v teorii ryadov.PhD Thesis Ross. Akad. Nauk Mat. Inst. (V. A. Steklov), Moskva (1993).
Reference: [17] Laflamme C.: Combinatorial aspects of $F_\sigma$ filters with an application to N-sets.Proc. Amer. Math. Soc. 125 (1997), 10 3019-3025. MR 1401747
Reference: [18] Miller A.W.: Some properties of measure and category.Trans. Amer. Math. Soc. 226 (1981), 93-144. Zbl 0472.03040, MR 0613787
Reference: [19] Repický M.: A family of permitted trigonometric thin sets.Proc. Amer. Math. Soc. 125 (1997), 1 137-144. MR 1343721
Reference: [20] Repický M.: Towers and permitted trigonometric thin sets.Real Anal. Exchange 21 (1995/96), 648-655. MR 1407277
Reference: [21] Repický M.: Mycielski ideal and the perfect set theorem.preprint, 2001. MR 2053988
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_42-2001-4_2.pdf 310.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo