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
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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