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The field structure of the real number system

Published online by Cambridge University Press:  09 April 2009

M. Venkataraman  and
T. Soundararajan
M. Venkataraman
Affiliation:
Madurai University Madurai, India
T. Soundararajan
Affiliation:
Madurai University Madurai, India
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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 3 , August 1967 , pp. 258 - 262
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Buch, V. B., ‘Topology of the open real line’, Journal of Gujarat University VI, 2, 187–198.Google Scholar
[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).Google Scholar
[3]Newman, M. H. A., Elements of the topology of plane sets of points (Cambridge 1951).Google Scholar
[4]Van der Waerden, B. L., Modern Algebra I (Frederick Ungar, New York 1949).Google Scholar