Abstract
We extend the results obtained in [1] to the case of arbitrary Banach spaces and manifolds. We give an example of a continuous bijective mapping with discontinuous inverse which acts in a Banach space and differs from the identical mapping only in an open unit ball. A criterion for a Banach manifold to be finite-dimensional is established in terms of the continuity of inverse operators.
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References
V. I. Savkin, “A criterion for Banach manifolds with a separable model to be finite-dimensional,”Ukr. Mat. Zh.,46, No. 8, 1099–1103 (1994).
H. Torunczyk, “Characterizing Hilbert space topology,”Fund. Math.,111, No. 3, 247–262 (1981).
K. Kuratowski,Topology [Russian translation], Vol. 1, Nauka, Moscow (1965).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1712–1713, December, 1995.
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Savkin, V.I. A criterion for Banach manifolds to be finite-dimensional. Ukr Math J 47, 1958–1959 (1995). https://doi.org/10.1007/BF01060971
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DOI: https://doi.org/10.1007/BF01060971