Approximation of continuous vector functions
We study the possibility of uniform approximation of continuous mappings of metric compact sets into metric spaces. Notions of “weak dimension” and “weak Kolmogorov width” are introduced to compare approximating properties of infinite-dimensional subspaces. For classes of mappings specified by the majorant of the modulus of continuity, we present bilateral estimates of “weak” widths that may coincide under certain conditions.
English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 11, pp 1585-1599.
Citation Example: Babenko V. F., Pichugov S. A. Approximation of continuous vector functions // Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1435–1448.