nLab
orbispace

Orbispaces are to topological spaces what orbifolds are to manifolds. An orbispace is a topological generalization of an orbifold, a class of topological stacks with locally finite stabilizers. A detailed but elementary approach via atlases can be found in

• Weimin Chen, A homotopy theory of orbispaces (arXiv)

and another approach is sketched in

• André Henriques, Orbispaces and orbifolds from the point of view of the Borel construction, a new definition (arXiv)