Spaces not distinguishing convergences
Repický, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 829-842 / Harvested from Czech Digital Mathematics Library

In the present paper we introduce a convergence condition $(\Sigma ')$ and continue the study of ``not distinguish'' for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.

Publié le : 2000-01-01
Classification:  03E17,  54A20,  54C30,  54C35,  54G99
@article{119215,
     author = {Miroslav Repick\'y},
     title = {Spaces not distinguishing convergences},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {829-842},
     zbl = {1067.54028},
     mrnumber = {1800160},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119215}
}
Repický, Miroslav. Spaces not distinguishing convergences. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 829-842. http://gdmltest.u-ga.fr/item/119215/

Bartoszyński T. Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. (1984) | MR 0719666

Bukovský L.; Recław I.; Repický M. Spaces not distinguishing pointwise and quasinormal convergence of real functions, Topology Appl. 41 (1991), 25-40. (1991) | MR 1129696

Bukovský L.; Recław I.; Repický M. Spaces not distinguishing convergences of real-valued functions, Topology Appl., to appear.

Van Douwen E.K. The integers and topology, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam, 1984, pp.111-167. | MR 0776622 | Zbl 0561.54004

Engelking R. General Topology, Państwowe Wydawnictwo Naukowe, Warszawa, 1977. | MR 0500779 | Zbl 0684.54001

Kada M.; Kamo S. New cardinal invariants related to pseudo-Dirichlet sets, preprint, 1996.

Kuratowski K. Topologie I, PWN, Warsaw, 1958. | Zbl 0849.01044

Miller A.W. Special subsets of the real line, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam, 1984, pp.201-233. | MR 0776624 | Zbl 0588.54035

Recław I. Metric spaces not distinguishing pointwise and quasinormal convergence of real functions, Bull. Polish Acad. Sci. Math. 45 (1997), 3 287-289. (1997) | MR 1477547