Convex, balanced and absorbing subsets of hypervector spaces

In this paper, we define convex, balanced and absorbing subsets of a hypervector space V over a field K, where K is considered R or C and give some examples of them. We prove that every subspace of a hypervector space is a convex and balanced subset. Also, for every regular equivalence relation ρ on a hypervector space V, we show that if A is a convex, balanced or an absorbing subset of V, then A/ρ is respectively a convex, balanced or an absorbing subset of a hypervector space V/ρ.