Lokalkreisförmige Vektorgruppen

We define locally circled vector groups as topological vector spaces over the discrete real or complex numberfield with a neighbourhoodbase of zero consisting of circled sets. Every topological vector space is a locally circled vector group. Topological vector groups and especially locally circled vector groups have useful applications to topological vector spaces and this paper is intended as an introduction to the theory of locally circled vector groups. Continuations including applications to topological vector spaces will follow. Here we study the structure of finite dimensional and locally compact vector groups, describe those locally circled vector groups which have a generating precompact circled set and finally prove some theorems about convex sets in these spaces.