This chapter is a study Quasi-Topological Structure (QTS) models in the frame of the Logic of Typical and Atypical (LTA). The quasi-topology structure (QTS) is a new mathematical structure. LTA is a logic that accounts for a finer categorization of the objects associated with the concepts. Epistemological motivations of the notions of the LTA and QTS are presented. It is sown how the QTS is realized in the extensions of LTA. Several examples from linguistics and other areas of social sciences and humanities are presented.