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.