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A topological characterization of norms on a nearfield

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Abstract

It is shown that every non-trivial norm on a nearfield F induces a topology T on F such that (F,T) is a locally bounded semitopological nearring with nonzero topological nilpotent elements and that any such topology can be obtained by a non-trivial norm.

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  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-6100, Darmstadt

    Emanuel Kolb

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  1. Emanuel Kolb
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Kolb, E. A topological characterization of norms on a nearfield. Results. Math. 21, 345–354 (1992). https://doi.org/10.1007/BF03323092

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  • DOI: https://doi.org/10.1007/BF03323092

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