The number of field topologies on countable fields
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- by Klaus-Peter Podewski PDF
- Proc. Amer. Math. Soc. 39 (1973), 33-38 Request permission
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.References
- J. Heine, Existence of locally unbounded topological fields, and field topologies which are not the intersection of bounded ring topologies, J. London Math. Soc. (2) 5 (1972), 481–487. MR 319958, DOI 10.1112/jlms/s2-5.3.481
- John O. Kiltinen, Inductive ring topologies, Trans. Amer. Math. Soc. 134 (1968), 149–169. MR 228474, DOI 10.1090/S0002-9947-1968-0228474-6
- Hans-Joachim Kowalsky, Beiträge zur topologischen Algebra, Math. Nachr. 11 (1954), 143–185 (German). MR 61099, DOI 10.1002/mana.19540110304
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 33-38
- MSC: Primary 12J99
- DOI: https://doi.org/10.1090/S0002-9939-1973-0311633-9
- MathSciNet review: 0311633