  Two finite words $u$ and $v$ are called abelian equivalent if each letter
occurs equally many times in both $u$ and $v$. The abelian closure
$\mathcal{A}(\mathbf{x})$ of an infinite word $\mathbf{x}$ is the set of
infinite words $\mathbf{y}$ such that, for each factor $u$ of $\mathbf{y}$,
there exists a factor $v$ of $\mathbf{x}$ which is abelian equivalent to $u$.
The notion of an abelian closure gives a characterization of Sturmian words:
among uniformly recurrent binary words, periodic and aperiodic Sturmian words
are exactly those words for which $\mathcal{A}(\mathbf{x})$ equals the shift
orbit closure $\Omega(\mathbf{x})$. Furthermore, for an aperiodic binary word
that is not Sturmian, its abelian closure contains infinitely many minimial
subshifts. In this paper we consider the abelian closures of well-known
families of non-binary words, such as balanced words and minimal complexity
words. We also consider abelian closures of general subshifts and make some
initial observations of their abelian closures and pose some related open
questions.
