SEQUENTIAL S ∗ - COMPACTNESS IN L - TOPOLOGICAL SPACES ∗ SHU - PING LI Mudanjiang

In this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S∗-compactness. If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S∗-compactness, and sequential S∗-compactness implies sequential F-compactness. The intersection of a sequentially S∗-compact L-set and a closed L-set is sequentially S∗-compact. The continuous image of an sequentially S∗compact L-set is sequentially S∗-compact. A weakly induced L-space (X, T ) is sequentially S∗-compact if and only if (X, [T ]) is sequential compact. The countable product of sequential S∗-compact L-sets is sequentially S∗-compact. 2000 Math. Subject Classification: Primary: 54A40.