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On Some Properties of Binary Relations

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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Some important notions in the theory of binary relations such as the relative product of two relations and the converse of a relation are defined in Whitehead and Russell’s “Principia mathematica” ([1]). McKinsey ([2]) and Tarski ([3]) gave their systems of postulates for the calculus of relations. Ore studied on equivalence relations ([4]) and Riguet on closures (fermeture) of relations ([5] and [6]), and they obtained remarkable results on the structure of these relations. The purpose of this paper is to examine the relative properties of some relations to each other, whose notions are closely related to the notions given by Riguet.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 161 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Whitehead, A. N. and Russell, B., Principia mathematica, vol. 1, Cambridge University Press, 1925 (2nd ed.).Google Scholar
[2] McKinsey, J. C. C., Postulates for the calculus of binary relations, Journ. of Sym. Log., vol. 5 (1940), pp. 85–97.Google Scholar
[3] Tarski, A., On the calculus of relations, Journ. of Sym. Log., vol. 6 (1941), pp. 73–89.Google Scholar
[4] Ore, O., Theory of equivalence relations, Duke Math. Journ., vol. 9 (1942), pp. 573–627.CrossRefGoogle Scholar
[5] Riguet, J., Relations binaires, fermetures, correspondances de Galois, Buletin de Société Mathematique de France, vol. 79 (1948), pp. 114–155.Google Scholar
[6] Riguet, J., Quelques propriétés des relations difonctionnelles, Comptes rendus hebmodaires des séances de l’Academie des Sciences, vol. 230 (1950), pp. 1999–2000.Google Scholar