## Abstract

We consider the problem of finding precise conditions for a map F between two Banach spaces X, Y to be a global homeomorphism.Using methods from covering space theory we reduce the global homeomorphism problem to one of finding conditions for a local homeomorphism to satisfy the “line lifting property.” This property is then shown to be equivalent to a limiting condition which we designate by (L). Thus we finally show that a local homeomorphism is a global homeomorphism if and only if (L) is satisfied. In particular we show that if a local homeomorphism is(i) proper (Banach-Mazur) or (ii) ò^{¥}_{0}inf_{x}_{£}_{s}l/(F'(x)]^{-1}ds = ¥ (Hadamard-Levy), then (L) is satisfied. Other analytic conditions are also given.

Original language | English (US) |
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Pages (from-to) | 169-183 |

Number of pages | 15 |

Journal | Transactions of the American Mathematical Society |

Volume | 200 |

DOIs | |

State | Published - 1974 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Keywords

- Covering space