@UNPUBLISHED{publication1, title = "Orbispaces as smooth stratified spaces", author = "{CRAINIC, Marius} and {MESTRE, Jo{\~{a}}o Nuno}", year = "2017-05-24", abstract = "We present some features of the smooth structure, and of the canonical smooth stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance - it allows us to talk about the canonical smooth stratification on the orbispace presented by the proper Lie groupoid. We make no claim to originality. The goal of these notes is simply to give a complementary exposition to those available, and to clarify some subtle points where the literature can sometimes be confusing, even in the classical case of proper Lie group actions. ", url = "http://www.mat.uc.pt/preprints/eng\_2017.html", note = "" }