Abstract
In this study, after giving the necessary definitions in the preliminaries and explaining the process that make this study necessary is explained in the introduction, in the third section, some types of open set that were previously defined in general topology and various non-standard topological spaces are presented and the relationships between them are explained with the help of a diagram. Then, the concept of neutrosophic af-open set is defined and its relations with other open set types are examined and their properties are investigated in neutrosophic topology. In the following sections, the concept of af-open set is generalized and different types of continuities are introduced using these new concepts of open set, and the connections between them are illustrated with examples and diagrams.
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