  In this paper we present another notion of a smooth manifold with corners and
relate it to the commonly used concept in the literature. Afterwards we
introduce complex manifolds with corners and show that if $M$ is a compact
(respectively complex) manifold with corners and $K$ is a smooth (respectively
complex) Lie group, then $C^{\infty}(M,K)$ (respectively
$C^{\infty}_{\C}(M,K)$) is a smooth (respectively complex) Lie group.
