Published in Topology and its Applications, Volume 159, Issue 17, November 1, 2012, pages 3583-3589.
The definitive version is available at https://doi.org/10.1016/j.topol.2012.08.032.
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sardʼs theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts.