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Bounded and relatively bounded sets

Published online by Cambridge University Press:  17 April 2009

Niel Shell
Affiliation:
The City College of New York (CUNY), Convent Avenue at 138th Street New York, NY 10031, USA
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All subsets of a field that are intersections of almost-orders of the field are characterised, and all ring topologies on a field which are not finer than any nontrivial locally bounded ring are characterised.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Dürbaum, H., “über die Ganzheitsbereiche bewerteter Korper”, Math. Z. 57 (1952), 8693.CrossRefGoogle Scholar
[2]Kowalsky, H.J., “Beiträge zur topologischen Algebra”, Math. Nachr. 11 (1954), 143185.CrossRefGoogle Scholar
[3]Mutylin, A.F., “An example of a nontrivial topologization of the field of rational numbers. Complete locally bounded fields”, Amer. Math. Soc. Transl. (2) 73 (1968), 159179.Google Scholar
[4]Nachbin, L., “On strictly minimal topological division rings”. Bull. Amer. Math. Soc. 55 (1949), 11281136.CrossRefGoogle Scholar
[5]Podewski, K.P., “The number of field topologies on countable fields”. Proc. Amer. Math. Soc. 39 (1973), 3338.CrossRefGoogle Scholar
[6]Shell, N., “Maximal and minimal ring topologies”, Proc. Amer. Math. Soc. 68 (1978), 2326.CrossRefGoogle Scholar
[7]Shell, N., “Connected and disconnected fields”, Topology Appl. (to appear).Google Scholar
[8]Weber, H., “Unabhängige Topologien, Zerlegung von Ringtopologien”, Math. Z. 180 (1982), 379393.CrossRefGoogle Scholar
[9]Więsław, w., “Independent topologies on fields”, Comment. Math. Univ. St. Paul 26 (1977), 201208.Google Scholar