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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A holomorphic function having a discontinuous inverse
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by T. J. Suffridge
Proc. Amer. Math. Soc. 31 (1972), 629-630
DOI: https://doi.org/10.1090/S0002-9939-1972-0284813-8
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Abstract:

An example is given of a function $f$ which is holomorphic in the open unit ball of ${l^\infty }$ and which extends in a natural way to the closed unit ball. The extended function gives a one-toone correspondence of the closed ball with itself but the inverse function fails to be continuous on the image of the open ball under the map $f$.
References
  • Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 629-630
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0284813-8
  • MathSciNet review: 0284813