Аннотация:
The purpose of this paper is to prove two theorems of convex geometry using the techniques of topology. The first theorem states that if, for a strictly convex body $K$, one may choose continuously a centrally symmetric section, then $K$ must be centrally symmetric. The second theorem states that if every section of a three-dimensional convex body $K$ through the origin has an axis of symmetry, then there is a section of $K$ through the origin which is a disk.