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Uniformly distributed sequences of positive integers in Baire’s space. (English) Zbl 0757.11023

The authors show some topological properties of the set of all uniformly distributed sequences of integers (straight-forward generalizations of known results).

MSC:

11K06 General theory of distribution modulo \(1\)
54E52 Baire category, Baire spaces
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References:

[1] ALEXANDROV P. S.: An Introduction to the General Theory of Sets and Functions. (Czech). NČSAV, Praha, 1954.
[2] HLAWKA E.: Theorie der Gleichverteilung. Bibliographisches Institut, Mannheim - Wien - Zürich, 1979. · Zbl 0406.10001
[3] KUIPERS L., NIEDERREITER H.: Uniform Distribution of Sequences. Wiley, New York, 1974. · Zbl 0281.10001
[4] LÁSZLÓ V., ŠALÁT T.: The structure of some sequence spaces, and uniform distribution (mod 1). Periodica Math. Hung. 10 (1979), 89-98. · Zbl 0396.10042 · doi:10.1007/BF02018376
[5] NAGATA, Jun-ti: Modern General Topology. North-Holland Publ. Comp., Amsterdam - London, 1974.
[6] NIVEN I.: Uniform distribution of sequences of integers. Trans. Amer. Math. Soc. 98 (1961), 52-61. · Zbl 0096.03102 · doi:10.2307/1993512
[7] SIKORSKI R.: Funkcje rzeczywiste I. PWN, Warszawa, 1958. · Zbl 0093.05603
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