CONTRACTIBILITY OF SlMPLE SCALING SETS.

In this paper, we show that the space of three-interval scaling functions with the induced metric of L² (ℝ) consists of three path-components each of which is contractible and hence, the first fundamental group of these spaces is zero. One method to construct simple scaling sets for L² (ℝ) and H²( ℝ) is described. Further, we obtain a characterization of a method to provide simple scaling sets for higher dimensions with the help of lower dimensional simple scaling sets and discuss scaling sets, wavelet sets and multiwavelet sets for a reducing subspace of L²(ℝn). The contractibility of simple scaling sets for different subspaces are also discussed. [ABSTRACT FROM AUTHOR]