ON CONNECTIONS BETWEEN VECTOR SPACES AND HYPERCOMPOSITIONAL STRUCTURES

Abstract

During his sort life, F. Marty, through three articles of his, introduced the notion of hypergroup.  W. Prenowitz utilized this structure in the study of Geometry.  This paper contributes to the methodology of connecting vector spaces with hypergroups.  Convexity is presented in hypercompositional algebra terms and we get to the theorems of Kakutani, Stone, Helly, Randon, Carathéodory and Steinitz, through more general theorems which are valid in hypergroups.