The concept of fuzzy soft set was introduced for the first time by Maji et al. in 2002, and was considered sharply from applicable aspects to theoretical aspects by a wide range of researchers. In this paper the concept of fuzzy soft norm over fuzzy
soft spaces has been considered and some properties of fuzzy soft normed spaces are studied. We also study the fuzzy soft topology over a crisp set by using the fuzzy soft subsets of it and the relationship between fuzzy soft topology and general topology is investigated. Fuzzy soft linear operator over fuzzy soft spaces is introduced and continuity of such operators is considered.
