In a fuzzy topology on a set X , the limit of a prefilter (i.e. a filter in the lattice [ 0 , 1 ] X ) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule “ lim ” which to any prefilter 𝔇 on X assigns, a function lim 𝔇 ∈ [ 0 , 1 ] X . We give necessary and sufficient conditions for the function 𝔇 → lim 𝔇 in order that it can be derived from a fuzzy topology.