  It is shown that, for an arbitrary free and minimal $\mathbb Z^n$-action on a
compact Hausdorff space $X$, the crossed product C*-algebra
$\mathrm{C}(X)\rtimes\mathbb Z^n$ always has stable rank one, i.e., invertible
elements are dense. This generalizes a result of Alboiu and Lutley on $\mathbb
Z$-actions.
  In fact, for any free and minimal topological dynamical system $(X, \Gamma)$,
where $\Gamma$ is a countable discrete amenable group, if it has the uniform
Rokhlin property and Cuntz comparison of open sets, then the crossed product
C*-algebra $\mathrm{C}(X)\rtimes\Gamma$ has stable rank one. Moreover, in this
case, the C*-algebra $\mathrm{C}(X)\rtimes\Gamma$ absorbs the Jiang-Su algebra
tensorially if, and only if, it has strict comparison of positive elements.
