Remarks on Steinhaus’ property and ratio sets of sets of positive integers

Tibor Šalát

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 1, page 175-183
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Šalát, Tibor. "Remarks on Steinhaus’ property and ratio sets of sets of positive integers." Czechoslovak Mathematical Journal 50.1 (2000): 175-183. <http://eudml.org/doc/30552>.

@article{Šalát2000,
abstract = {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.},
author = {Šalát, Tibor},
journal = {Czechoslovak Mathematical Journal},
keywords = {ratio set; Steinhaus' property; uniform density of set},
language = {eng},
number = {1},
pages = {175-183},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on Steinhaus’ property and ratio sets of sets of positive integers},
url = {http://eudml.org/doc/30552},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Šalát, Tibor
TI - Remarks on Steinhaus’ property and ratio sets of sets of positive integers
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 175
EP - 183
AB - 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.
LA - eng
KW - ratio set; Steinhaus' property; uniform density of set
UR - http://eudml.org/doc/30552
ER -

References

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  11. Über die Cantorsche Reihen, Czechoslovak Math. J. 18(93) (1968), 25–56. (1968) 
  12. 10.4064/aa-15-3-273-278, Acta Arith. 15 (1969), 273–278. (1969) MR0242756DOI10.4064/aa-15-3-273-278
  13. 10.4064/aa-19-1-63-78, Acta Arithm. 19 (1971), 63–78. (1971) Zbl0218.10071MR0292788DOI10.4064/aa-19-1-63-78
  14. 10.2307/2974957, Amer. Math. Monthly 102 (1995), 347–349. (1995) Zbl0828.11004MR1328019DOI10.2307/2974957
  15. Elementary Theory of Numbers, PWN, Warszawa, 1964. (1964) MR0175840

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