  We propose a new definition of preimage entropy dimension for continuous maps
on compact metric spaces, investigate fundamental properties of the preimage
entropy dimension, and compare the preimage entropy dimension with the
topological entropy dimension. The defined preimage entropy dimension holds
various basic properties of topological entropy dimension, for example, the
preimage entropy dimension of a subsystem is bounded by that of the original
system and topologically conjugated systems have the same preimage entropy
dimension. Also, we discuss the relation between the preimage entropy dimension
and the preimage entropy.
