Strong-III Nβ-compactness in L-topological spaces

In this paper, by means of semi-pre-open strong β_α-cover and semi-pre-open β_α-cover, the concept of strong-III Nil-compactness is introduced for an arbitrary L-subset. The strong-III N_β-compactness is different from SP-compactness. But when L = [0,1], strong-III N_β-compactness is equivalent to SP-compactness.