Remarks on R-density of sets of numbers

Rok, strany: 1997, 159 - 165

If $A\subseteq\Bbb N$ or $A\subseteq(0,+∞)$, then we put $R(A)=\{\frac a b:a,b\in A\}$. The set $A$ is said to be $(R)$-dense provided that the set $R(A)$ is dense in $(0,+∞)$. In the paper a sufficient condition for $(R)$-density of sets $A\subseteq\Bbb N$ is given using the concept of uniform density of sets. Further the answers are given to two questions formulated by O. Strauch concerning the decomposition $\Bbb N=A\cup B$ with non $(R)$-dense sets $A, B$ and the relation between $(R)$-density of a sequence $1<a₁<a₂<…<a_n…$, $a_n\to+∞$ of real numbers and the sequence $a\leqslant[a₁]\leqslant [a₂]\leqslant…\leqslant[a_n]≤…$.

ISO 690:

Bukor, J., Šalát, T., Tóth, J. 1997. Remarks on R-density of sets of numbers. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 159-165. 1210-3195.

APA:

Bukor, J., Šalát, T., Tóth, J. (1997). Remarks on R-density of sets of numbers. Tatra Mountains Mathematical Publications, 11(2), 159-165. 1210-3195.