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). |