Globalizing fibrations by schedules.

TitleGlobalizing fibrations by schedules.
Publication TypeJournal Article
Year of Publication1988
AuthorsDyer E, Eilenberg S
JournalFundam. Math.
Volume130
Pagination125-136
Keywordsglobalization 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).