Ivanov O. Spherical Gauss type mappings in problems of partition of the sets

The thesis is devoted to the construction of spherical Gauss mapping and study of their properties with respect to applications to the problem of K. Borsuk partition sets into parts of smaller diameter . These new sufficient conditions for accessories sets of constant width with irregular boundary to class of Borsuk. These results significantly clarify the description of the class Borsuk in multidimensional spaces with Euclidean norm. First results, specifying the class of Borsuk's sets on multi non-Euclidean spaces. Improved results Shpraha case splitting sets fixed diameter class into subclasses according to some criterion ( in the case of each subclass improved outcome ).