WAVELET SETS IN R-N

A congruency theorem is proven far an ordered pair of groups of homeom orphisms of a metric space satisfying an abstract dilation-translation relationship. A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive matrix dilations on L-2(R-n). Moreover for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel s tructure of R-n.