  All wavelets can be associated to a multiresolution like structure, i.e. an
incr easing sequence of subspaces of L^2(R). We consider the interaction of a
wavel et and the translation operator in terms of which of the subspaces in
this multi resolution like structure are invariant under the translation
operator. This ac tion defines the notion of the translation invariance
property of order n. In this paper we show that wavelets of all levels of
translation invariance exist, first for the classic case of dilation by 2, and
then for arbitrary integral di lation factors.
