In this paper we define, for fuzzy topology, notions corresponding to
finite-to-one and k-to-one maps. We study the relationship between the
se new fuzzy maps and various kinds of fuzzy perfect maps. Also, we sh
ow the invariance and the inverse invariance under the various kinds o
f fuzzy perfect maps (and the finite-to-one fuzzy maps), of different
properties of fuzzy topological spaces.