Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces.

We establish a number of theorems of geometric approximation theory in asymmetrically normed spaces. Sets with continuous selection of the near-best approximation operator are studied and properties of such sets are discussed in terms of -solar points and the distance function. A result on the coincidence of the classes of - and -suns in asymmetric spaces is given. An asymmetric analogue of the Kolmogorov criterion for an element of best approximation for suns, strict suns, and -suns is put forward. [ABSTRACT FROM AUTHOR]