Homeomorphisms between Banach spaces
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 by Roy Plastock PDF
 Trans. Amer. Math. Soc. 200 (1974), 169183 Request permission
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 (BanachMazur) or (ii) $\int _0^\infty {{{\inf }_{x \leqslant s}}} 1/{[F’(x)]^{  1}}ds = \infty$ (HadamardLevy), then $(L)$ is satisfied. Other analytic conditions are also given.References

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Additional Information
 © Copyright 1974 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 200 (1974), 169183
 MSC: Primary 58C15; Secondary 57A20
 DOI: https://doi.org/10.1090/S00029947197403561226
 MathSciNet review: 0356122