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 \mathbb{R} or \mathbb{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 \rho on a hypervector space V, we  show that if A is a convex, balanced or an absorbing subset of V, then A/\rho is respectively a convex, balanced or an absorbing subset of a hypervector space V/\rho.

کلیدواژه ها:

Hypervector space ، Convex set ، Balanced set ، Absorbing set