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Proceedings of the American Mathematical Society

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

 

 

On a problem of L. Nachbin


Author: Thomas J. Jech
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
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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

$\displaystyle r({b_1},{b_2}) \leqslant t({b_1}) \cdot t({b_2})\quad {\text{for all}}\;{b_1},{b_2} \in B.$


References [Enhancements On Off] (What's this?)

  • [1] 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, Amsterdam, 1977, pp. 31–74. North-Holland Math. Studies, Vol. 12, Notas de Mat., No. 54. MR 0473817

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565368-1
Article copyright: © Copyright 1980 American Mathematical Society