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Proceedings of the American Mathematical Society

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

 

 

On the number of locally bounded field topologies


Author: Jo-Ann D. Cohen
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
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Abstract: Kiltinen has proven that there exist $ {2^{\left\vert F \right\vert}}$ 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\vert F \right\vert}}$ normable, locally bounded field topologies on $ F$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0727234-1
Article copyright: © Copyright 1984 American Mathematical Society