θθ-Compactness in L-topological spaces

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and e∞e∞ theory. In 2005, Caldas and Jafari have introduced θθ-compact fuzzy topological spaces. In this paper, the concepts of  θθ-compactness, countable  θθ-compactness and the  θθ-Lindelöf property are introduced and studied in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of  θ-openL-sets and their inequalities. They does not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by  θ-closedL-sets and their inequalities. When L is a completely de Morgan algebra, their many characterizations are presented.