Abstract
Apart from their applications to almost all sectors of the human activity, fuzzy mathematics is also importantly developed on a theoretical basis providing useful links even to classical branches of pure mathematics, like Algebra, Analysis, Geometry, Topology, etc. The present paper comes across the steps that enabled the extension of the concept of topological space, the most general category of mathematical spaces, to fuzzy structures. Fuzzy and soft topological spaces are introduced in particular, the fundamental concepts of limits, continuity, compactness and Hausdorff space are defined on them and examples are provided illustrating them.
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