Abstract
The aim of this study is to dene fuzzy soft topology which will be compatible to the fuzzy soft theory and investigate some of its fundamental properties. Firstly, we recall some basic properties of fuzzy soft sets and then we give the denitions of cartesian product of two fuzzy soft sets and projection mappings. Secondly, we introduce fuzzy soft topology and fuzzy soft continuous mapping. Moreover, we induce a fuzzy soft topology after given the denition of a fuzzy soft base. Also, we obtain an initial fuzzy soft topology and give the denition of product fuzzy soft topology. Finally, we prove that the category of fuzzy soft topological spaces FSTOP is a topological category over SET:
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