  Piecewise affine functions on subsets of $\mathbb R^m$ were studied in
\cite{Ovchinnikov:02,Aliprantis:06a,Aliprantis:07a,Aliprantis:07}. In this
paper we study a more general concept of a locally piecewise affine function.
We characterize locally piecewise affine functions in terms of components and
regions. We prove that a positive function is locally piecewise affine iff it
is the supremum of a locally finite sequence of piecewise affine functions. We
prove that locally piecewise affine functions are uniformly dense in $C(\mathbb
R^m)$, while piecewise affine functions are sequentially order dense in
$C(\mathbb R^m)$.
  This paper is partially based on \cite{Adeeb:14}.
