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The classical mathematical theories have their difficulties which are pointed out in [18] for the solution complicated problems in engineering and environment. To overcome these difficulties, Molodtsov [18] introduced the concept of soft set as a new mathematical tool. Furthermore, D. Pei and D. Miao [22] showed that soft sets are a class of special information systems. In [9] for the soft set theory: new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets are introduced and studied. Moreover, the theory of soft topological spaces is investigated. This paper continues the study of the theory of soft topological spaces and presents for this theory new definitions, characterizations, and results concerning separation axioms, convergence, Cartesian product, soft q -topology, and soft q -continuity.

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