The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case. These results are required for further applications to holonomy and monodromy. (C) 2002 Elsevier Science B.V. All rights reserved.
C1 Univ Coll N Wales, Sch Informat, Math Div, Bangor LL57 1UT, Gwynedd, Wales.
Univ Inonu, Fac Sci & Art, Dept Math, Malatya, Turkey.
Erciyes Univ, Fac Sci & Art, Dept Math, Kayseri, Turkey.