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A criterion for Banach manifolds with a separable model to be finite-dimensional

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Abstract

We give an example of a continuous bijective mapping with a discontinuous inverse which acts in a separable Banach space and differs from the identical mapping only in an open unit ball. A criterion for Banach manifolds with a separable model to be finite-dimensional is established in terms of the continuity of inverse operators.

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References

  1. A. Dold,Lectures on Algebraic Topology [Russian translation], Mir, Moscow (1976).

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Authors and Affiliations

  1. Kiev Polytechnical Institute, Kiev

    V. I. Savkin

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  1. V. I. Savkin
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1099–1103, August, 1994.

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Savkin, V.I. A criterion for Banach manifolds with a separable model to be finite-dimensional. Ukr Math J 46, 1210–1214 (1994). https://doi.org/10.1007/BF01056184

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  • DOI: https://doi.org/10.1007/BF01056184

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