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Summary:
This paper is closely related to an earlier paper of the author and W. Narkiewicz (cf. [7]) and to some papers concerning ratio sets of positive integers (cf. [4], [5], [12], [13], [14]). The paper contains some new results completing results of the mentioned papers. Among other things a characterization of the Steinhaus property of sets of positive integers is given here by using the concept of ratio sets of positive integers.
References:
[1] T. M. Apostol: Introduction to Analytic Number Theory. Springer-Verlag, New York-Heidelberg-Berlin, 1976. MR 0434929 | Zbl 0335.10001
[2] T. C. Brown, A. R. Freedman: Arithmetic progressions in lacunary sets. Rocky Mountain J. Math. 17 (1987), 587–596. DOI 10.1216/RMJ-1987-17-3-587 | MR 0908265
[3] T. C. Brown, A. R. Freedman: The uniform density of sets of integers and Fermat’s last theorem. C. R. Math. Rep. Acad. Sci. Canada XII (1990), 1–6. MR 1043085
[4] J. Bukor, M. Kmeťová, J. Tóth: Notes on ratio sets of sets of natural numbers. Acta Math. (Nitra) 2 (1995), 35–40.
[5] D. Hobby, D. M. Silberger: Quotients of primes. Amer. Math. Monthly 100 (1993), 50–52. DOI 10.2307/2324814 | MR 1197643
[6] J. Nagata: Modern General Topology. North-Holland Publ. Comp. Amsterdam-London-Groningen-New York, 1974. MR 0474164
[7] W. Narkiewicz, T. Šalát: A theorem of H. Steinhaus and $(R)$-dense sets of positive integers. Czechoslovak Math. J. 34(109) (1984), 355–361. MR 0761418
[8] H. H. Ostmann: Additive Zahlentheorie I. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956. MR 0098721 | Zbl 0072.03101
[9] T. Šalát: Cantorsche Entwicklungen der reellen Zahlen und das Husdorffsche. Mass. Publ. Math. Inst. Hung. Acad. Sci. 6 (1961), 15–41. MR 0147465
[10] T. Šalát: On Hausdorff measure of linear sets (Russian). Czechoslovak Math. J. 11(86) (1961), 24–56. MR 0153802
[11] T. Šalát: Über die Cantorsche Reihen. Czechoslovak Math. J. 18(93) (1968), 25–56.
[12] T. Šalát: On ratio sets of sets of natural numbers. Acta Arith. 15 (1969), 273–278. DOI 10.4064/aa-15-3-273-278 | MR 0242756
[13] T. Šalát: Quotientbasen und $(R)$-dichte Mengen. Acta Arithm. 19 (1971), 63–78. DOI 10.4064/aa-19-1-63-78 | MR 0292788 | Zbl 0218.10071
[14] P. Starni: Answers to two questions concerning quotients of primes. Amer. Math. Monthly 102 (1995), 347–349. DOI 10.2307/2974957 | MR 1328019 | Zbl 0828.11004
[15] W. Sierpiński: Elementary Theory of Numbers. PWN, Warszawa, 1964. MR 0175840
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