The concept of a fuzzy set was introduced by Zadeh , and later Chang  defined fuzzy topological spaces. These spaces and their generalizations are later studied by several authors, one of which, developed by Šostak [11, 12], used the idea of degree of openness. This type of generalization of fuzzy topological spaces was later rephrased by Chattopadhyay et al. , and by Ramadan . In 1983, Atanassov introduced the concept of “Intuitionistic fuzzy set” [1, 2]. Using this type of generalized fuzzy set, Çoker [5, 8] defined “Intuitionistic fuzzy topological spaces.” In 1996, Çoker and Demirci  introduced the basic definitions and properties of intuitionistic fuzzy topological spaces in Šostak’s sense, which is a generalized form of “fuzzy topological spaces” developed by Šostak [11, 12]. In this paper, we introduce the follwing concepts: fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological spaces in view of the definition of Šostak.