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- W3146828877 abstract "K.-P. Podewski has recently proven that every countable infinite field admits 2210 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 221 field topologies. By purely set theoretic considerations, it then follows that there are 221F1 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 Podewski's work on countable fields is generalized in a final theorem which states that a field F of infinite transcendence degree admits 22'F' field topologies which fail to be suprema of locally bounded ring topologies." @default.
- W3146828877 created "2021-04-13" @default.
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- W3146828877 date "2016-01-01" @default.
- W3146828877 modified "2023-09-25" @default.
- W3146828877 title "ON THE NUMBER OF FIELD TOPOLOGIES ON AN INFINITE FIELD" @default.
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