|Title||Globalizing fibrations by schedules.|
|Publication Type||Journal Article|
|Year of Publication||1988|
|Authors||Dyer E, Eilenberg S|
|Keywords||globalization theorems for Hurewicz fibrations, inversible fibrations, numerable covering, scheduling operation|
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).