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The field structure of the real number system

  • M. Venkataraman (a1) and T. Soundararajan (a1)
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It is well-known that the real number system can be characterised as a topological space [1], [3], as an ordered set [2], and as an ordered field [4]. It is the aim of this note to give two characterisations of the system purely as a field (see Theorems 4 and 9) without any extra notion of order, topology, et cetera.

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References
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[1]Buch, V. B., ‘Topology of the open real line’, Journal of Gujarat University VI, 2, 187198.
[2]Huntington, E. V., The continuum and other types of serial order, with an introduction to Cantor's transfinite numbers (2nd edition, Dover, New York 1955).
[3]Newman, M. H. A., Elements of the topology of plane sets of points (Cambridge 1951).
[4]Van der Waerden, B. L., Modern Algebra I (Frederick Ungar, New York 1949).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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