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- W4230704893 abstract "K.-P. Podewski has recently proven that every countable infinite field admits ${2^{{}_2{aleph _0}}}$ different field topologies. Using methods of valuation theory, it is proven that every uncountable field, and more generally, every field $F$ of infinite transcendence degree over some subfield, admits ${2^{{2^{|F|}}}}$ field topologies. By purely set theoretic considerations, it then follows that there are ${2^{{2^{|F|}}}}$ field topologies on any infinite field $F$, no two of which are topologically isomorphic. This latter result is then generalized to any infinite commutative ring without proper zero-divisors. A further aspect of Podewskiâs work on countable fields is generalized in a final theorem which states that a field $F$ of infinite transcendence degree admits ${2^{{2^{|F|}}}}$ field topologies which fail to be suprema of locally bounded ring topologies." @default.
- W4230704893 created "2022-05-11" @default.
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- W4230704893 date "1973-09-01" @default.
- W4230704893 modified "2023-10-16" @default.
- W4230704893 title "On the Number of Field Topologies on an Infinite Field" @default.
- W4230704893 doi "https://doi.org/10.2307/2038626" @default.
- W4230704893 hasPublicationYear "1973" @default.
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