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
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