A New Countable Compactness of L-fuzzy Topological Spaces

In this paper, the conceptions of countable S-compacuness and countable S-compactness are defined in L-fuzzy topological spaces. And many properties or characterizations of countable S-compactness (countable S-compactness) are presented. Moreover the relationships between countable compactness and S-Lindelf property are studied, and then draw a lots of conclusions such as, a countable S-compact space with S-Lindelf property is a S-compact space.