This is an announcement for the paper "Complete sets and completion of sets in Banach spaces" by Horst Martini, Pier Luigi Papini, and Margarita Spirova. Abstract: In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and centers. The results are illustrated by several examples. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 46B99, 52A05, 52A20, 52A21 Submitted from: margarita.spirova@mathematik.tu-chemnitz.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.0789 or http://arXiv.org/abs/1308.0789