Let \textbf{TOP} denote the category of topological spaces; [0, 1]-\textbf{TOP} the category of [0, 1]-topological spaces; \textbf{FYS} the category of fuzzifying topological spaces; and [0, 1]-\textbf{FTOP} the category of Šostak fuzzy topological spaces. The authors construct a pair of functors \(\omega:\) \textbf{FYS}\(\to [0, 1]\)-\textbf{FTOP} and \(\iota:\) [0, 1]-\textbf{FTOP}\(\to \)\textbf{FYS}. These two functors behave in a way similar to the Lowen functors: \(\omega: \)\textbf{TOP}\(\to [0, 1]\)-\textbf{TOP} and \(\iota:\) [0, 1]-\textbf{TOP}\(\to \)\textbf{TOP}. Some basic properties of these two functors are discussed.