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Families of sets on a finite set

Part of: Classical measure theory Designs and configurations

Published online by Cambridge University Press:  09 April 2009

C. J. Ashman  and
V. Ficker
C. J. Ashman
Affiliation:
Department of Mathematics University of NewcastleNewcastle, N.S.W.Australia2308
V. Ficker
Affiliation:
Department of Mathematics University of NewcastleNewcastle, N.S.W.Australia2308
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Abstract

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V. Krishnamurthy has shown that on a finite set X all topologies can be mapped into a certain set of matrices of zeros and ones. In this paper it is shown that all lattices, algebras and rings on a finite set X can be mapped onto particular sets of matrices of zeros and ones.

MSC classification

Secondary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets 05B20: Matrices (incidence, Hadamard, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 3 , December 1984 , pp. 405 - 412
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Evans, J. W., Harary, F. and Lynn, M. S., ‘On the computer enumeration of finite topologies’, Comm. ACM 10 (1967), 295–298.CrossRefGoogle Scholar
[2]Krishnamurthy, V., ‘On the number of topologies on a finite set’, Amer. Math. Monthly 73 (1966), 154–157.CrossRefGoogle Scholar
[3]Levinson, H. and Silverman, R., ‘Topologies on finite sets II’, Proc. Tenth S-E Conf. Comb. Graph Theory Comput. (1979), pp. 699–712.Google Scholar