### A geometrical solution of a problem on wavelets

We prove the existence of nonseparable, orthonormal, compactly supported wavelet bases for ${L}^{2}\left({\mathbb{R}}^{2}\right)$ of arbitrarily high regularity by using some basic techniques of algebraic and differential geometry. We even obtain a much stronger result: “most” of the orthonormal compactly supported wavelet bases for ${L}^{2}\left({\mathbb{R}}^{2}\right)$, of any regularity, are nonseparable