we discuss the path-connectivity between two
$s$-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a $\sigma$-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping
defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two $s$-elementary wavelets.