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Proceedings of the American Mathematical Society

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

 

 

The number of field topologies on countable fields


Author: Klaus-Peter Podewski
Journal: Proc. Amer. Math. Soc. 39 (1973), 33-38
MSC: Primary 12J99
MathSciNet review: 0311633
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Abstract: J. O. Kiltinen proves that every infinite field admits a nondiscrete, Hausdorff field topology. In this note it is shown that every countable field $ K$ admits $ {2^{{2^{{\aleph _0}}}}}$ many field topologies, which even fail to be the join of locally bounded ring topologies.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0311633-9
Article copyright: © Copyright 1973 American Mathematical Society