Cantor set and interpolation / O. D. Frolkina. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 6. P. 26-32 [Moscow Univ. Math. Bulletin. Vol. 64, N 6, 2009. P. 253-258].

In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions \mathbb R\to\mathbb R. In particular, he proved that there exists a continuous function \mathbb R\to \mathbb R which in some sense "interpolates" all sequences (x_n)_{n\in\mathbb Z} \in [0,1]^{\mathbb Z} "simultaneously." In 2005, M.R. Naulin and C. Uzcátegui unifyed and generalized Benyamini's results. In this paper, the case of topological spaces X and Y with an abelian group acting on X is considered. A similar problem of "simultaneous interpolation" of all "generalized sequences" using continuous mappings X\to Y is posed. Further generalizations of Naulin–Uncátegui theorems, in particular, multidimensional analogues of Benyamini's results are obtained.

Key words: \mathfrak G-space, continuous mapping, interpolation, Cantor set.