Every ball centered at the origin 0 of a normed space whethe

Every ball centered at the origin 0 of a normed space, whether open or closed , is balanced and absorbing ?

While absorbing means if for each x in X there is a positive number s_x such that x in tA whenever t>s_x.

Solution

Every ball centered at the origin 0 of a open normed space is balanced and absorbing; but, in a closed normed space it is balanced but not absorbing.