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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a problem of L. Nachbin
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by Thomas J. Jech PDF
Proc. Amer. Math. Soc. 79 (1980), 341-342 Request permission

Abstract:

If B is an uncountable set then there is a function $r:B \times B \to {{\mathbf {R}}_ + }$ for which there is no function $t:B \to {{\mathbf {R}}_ + }$ such that \[ r({b_1},{b_2}) \leqslant t({b_1}) \cdot t({b_2})\quad {\text {for all}}\;{b_1},{b_2} \in B.\]
References
  • Jorge Alberto Barroso, Mário C. Matos, and Leopoldo Nachbin, On holomorphy versus linearity in classifying locally convex spaces, Infinite dimensional holomorphy and applications (Proc. Internat. Sympos., Univ. Estadual de Campinas, São Paulo, 1975) North-Holland Math. Studies, Vol. 12; Notas de Mat., No. 54, North-Holland, Amsterdam, 1977, pp. 31–74. MR 0473817
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 79 (1980), 341-342
  • MSC: Primary 04A20; Secondary 26A12, 46A05
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0565368-1
  • MathSciNet review: 565368