Compactness in Countable Fuzzy Topological Space

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other related concepts like Lindelöf property, countable compactness are defined and studied in the countable fuzzy topological space.