A new notion of fuzzy compactness in L-topological spaces

In this paper, a new notion of compactness is introduced in L-topological spaces by means of βa-open cover and Qa-open cover, which is called S*-compactness. Ultra-compactness implies S*-compactness. S*-compactness implies fuzzy compactness, but fuzzy compactness need not imply S*-compactness. If L=[0,1], then strong compactness implies S*-compactness, but S*-compactness need not imply strong compactness. The intersection of an S*-compact L-set and a closed L-set is S*-compact. The continuous image of an S*-compact L-set is S*-compact. A weakly induced L-space (X, I) is S*-compact if and only if(X, [I]) is compact. The Tychonoff Theorem for S*-compactness is true. The L-fuzzy unit interval is S*-compact. Moreover S*-compactness can also be characterized by nets.