  Inspired by work of Borzellino and Brunsden, we generalize the notion of a
submanifold identifying a natural and sufficiently general condition which
guarantees that a subset of an (effective) orbifold carries itself a canonical
induced orbifold structure. We illustrate the strength of this approach
generalizing typical constructions of submanifolds to the orbifold setting
using embeddings, proper group actions and the idea of transversality.

Geometric Topology;Differential Geometry;Metric Geometry