In this paper, we try to answer an open question raised by Han and Larson,
which asks about the characterization of frame wavelet sets. We completely
characterize tight frame wavelet sets. We also obtain some necessary condit
ions and some sufficient conditions for a set E to be a (general) frame wav
elet set. Some results are extended to frame wavelet functions that are not
defined by frame wavelet set. Several examples are presented and compared
with some known results in the literature.