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,T) is S∗-compact if and only if (X,[T]) 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.