Abstract

In this paper, we obtain that the space $\Cal{W}$ of orthonormal wavelets enjoys the complete invariance property with respect to homeomorphisms. Further, it is obtained that the cylinder, the cone and the suspension of $\Cal{W}$ possess the complete invariance property. Certain subspaces of $\Cal{W}$ are also considered in this connection.

Keywords: Wavelets; MSF Wavelets; MRA Wavelets; CIP; CIPH; dimension function.

MSC: 42C15, 42C40, 54H25

Pages:  183$-$188     

Volume  62 ,  Issue  2 ,  2010