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Properties of finite character of independence spaces

Part of: Designs and configurations

Published online by Cambridge University Press:  26 February 2010

M. J. Piff
M. J. Piff
Affiliation:
The Mathematical Institute, OxfordDepartment of Pure Mathematics, University of Sheffield.
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Extract

The purpose of this paper is to demonstrate that a number of properties of independence spaces are of finite character, thus making it possible to easily generalise known theorems for finite spaces, or matroids, to independence spaces on infinite sets.

MSC classification

Secondary: 05B35: Matroids, geometric lattices
Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 201 - 208
Copyright
Copyright © University College London 1971

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References

1de Sousa, J. and Welsh, D. J. A., “A characterization of binary transversal structures ” J. Math. Anal. Applic. (to appear).Google Scholar
2Harary, F. and Welsh, D., Matroids versus graphs, the many facets of graph theory (Springer-Verlag, 1969), 155–170.CrossRefGoogle Scholar
3Mason, J., Doctoral thesis (Wisconsin, 1969).Google Scholar
4Minty, G. J., “On the axiomatic foundations of the theories of directed linear graphs, electrical networks and network programming ”, J. Math. Mech., 15 (1966), 485–520.Google Scholar
5Mirsky, L., “A hierarchy of structures ”, Some aspects of transversal theory, Seminar, Sheffield, 1967.Google Scholar
6Rado, R., “Axiomatic treatment of rank in infinite sets ”, Canad. J. Math., 1 (1949), 337–343.CrossRefGoogle Scholar
7Tutte, W. T., “Lectures on matroids ”, J . Res. Nat. Bur. Stand., 69B (1965), 1–47.Google Scholar
8Vamos, P., “On the representation of independence structures ” (to appear).Google Scholar
9Whitney, H., “On the abstract properties of linear dependence ”, Amer. J. Math., 57 (1935) 509–533.CrossRefGoogle Scholar