Cantor Set and Interpolation / O.D. Frolkina // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 6. P. 26-32 [Moscow Univ. Math. Bulletin. Vol. 64, No 6, 2009. P. 253-258.]
In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions R→R. In particular, he proved that there exists a continuous function R→R which in some sense "interpolates" all sequences (xn)n∈Z ∈ [0,1]Z "simultaneously." In 2005, M.R. Naulin and C. Uzcategui unified 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→ Y is posed. Further generalizations of Naulin-Uncategui theorems, in particular, multidimensional analogues of Benyamini's results are obtained.
Key words: G-space, continuous mapping, interpolation, Cantor set.