In that paper, the concept of (i, j) − mX − Î ²âˆ’exterior sets in a biminimal structurespace (BSS) and a biminimal structure subspace (BSs) were introduced. Based on properties of BSS and BSs, some new notions and several properties of those sets dealing with this space were obtained in both of BSS and BSs. Some examples were given to illustrate the effectiveness of these results.