Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series

• Date: 2007
• Main Authors: Baranovskyi, O. M., Pratsiovytyi, M. V., Torbin, H. M., Барановський, О. М., Працьовитий, М. В., Торбін, Г. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3379
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study topological and metric properties of the set $$C\left[\overline{O}^1, \{V_n\}\right] = \left\{x:\; x= ∑_n \frac{(−1)^{n−1}}{g_1(g_1 + g_2)…(g_1 + g_2 + … + g_n)},\quad g_k ∈ V_k ⊂ \mathbb{N}\right\}$$ with certain conditions on the sequence of sets $\{V_n\}$. In particular, we establish con...