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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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On the number of locally bounded field topologies
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by Jo-Ann D. Cohen
Proc. Amer. Math. Soc. 90 (1984), 207-210
DOI: https://doi.org/10.1090/S0002-9939-1984-0727234-1

Abstract:

Kiltinen has proven that there exist ${2^{\left | F \right |}}$ first countable, locally bounded field topologies (the maximum number possible) on a field $F$ of infinite transcendence degree over its prime subfield. We consider those fields $F$ of countable transcendence degree over its prime subfield $E$. In particular it is shown that if the characteristic of $F$ is zero and the transcendence degree of $F$ over $E$ is nonzero or if $F$ is a field of prime characteristic and the transcendence degree of $F$ over $E$ is greater than one, then there exist ${2^{\left | F \right |}}$ normable, locally bounded field topologies on $F$.
References
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Bibliographic Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 207-210
  • MSC: Primary 12J05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0727234-1
  • MathSciNet review: 727234