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.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1435–1448, November, 1994.