Abstract
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 ∞ theory. In 2005, Caldas and Jafari have introduced θ - compact fuzzy topological spaces. In this paper, the concepts of θ - compactness, countable θ - compactness and the θ - 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 - open L - 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 - closed L - sets and their inequalities. When L is a completely de Morgan algebra, their many characterizations are presented.
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