The crossed product of C(X) by a free minimal action of R
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In this dissertation, we will study the crossed product C*-algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable recursive subhomogeneous algebras (SRSHAs), which differ from recursive subhomogeneous algebras introduced by N. C. Phillips in that the irreducible representations of SRSHAs are infinite dimensional instead of finite dimensional. We show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and non-vanishing have topological stable rank one. We then construct C*-subalgebras of the crossed product that are analogous to the C*-subalgebras in the studies of free minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. Finally, we prove that these C*-algebras are in fact simple inductive limits of SRSHAs in which the connecting maps are injective and non-vanishing. Thus these C*-subalgebras have topological stable rank one.