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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Homeomorphisms between Banach spaces
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by Roy Plastock PDF
Trans. Amer. Math. Soc. 200 (1974), 169-183 Request permission


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) $\int _0^\infty {{{\inf }_{||x|| \leqslant s}}} 1/||{[F’(x)]^{ - 1}}||ds = \infty$ (Hadamard-Levy), then $(L)$ is satisfied. Other analytic conditions are also given.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 200 (1974), 169-183
  • MSC: Primary 58C15; Secondary 57A20
  • DOI:
  • MathSciNet review: 0356122