# Globalizing fibrations by schedules.

 Title Globalizing fibrations by schedules. Publication Type Journal Article Year of Publication 1988 Authors Dyer E, Eilenberg S Journal Fundam. Math. Volume 130 Pagination 125-136 Keywords globalization theorems for Hurewicz fibrations, inversible fibrations, numerable covering, scheduling operation Abstract Given a locally finite covering of a space X by numerable open sets, the authors construct a continuous scheduling'' operation that breaks up every path in X into subpaths each of which is contained in some element of the covering. The motive is to take a fresh look at globalization theorems for Hurewicz fibrations. Such a theorem follows as an easy corollary of the above result. The method is well suited to deal with fibrations carrying extra structure, such as inversible fibrations (where path lifting defines a homeomorphism between two fibers).