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Lattices of zero-sets

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

S. Broverman
S. Broverman
Affiliation:
Department of Mathematics University of TorontoOntario M5S 1A1Canada
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Abstract

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Characterizations are obtained of those lattices that are isomorphic to the lattice of zero-sets of the following types of Tychonoff spaces: (i) compact (Hausdorff), (ii) Lindelöf, (iii) realcompact and normal, (iv) realcompact.

MSC classification

Secondary: 54H99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 189 - 194
Copyright
Copyright © Australian Mathematical Society 1978

References

REFERENCES

Birkhoff, G. (1948), Lattice Theory (Amer. Math. Soc. Colloq. Publ., New York).Google Scholar
Gillman, L. and Jerison, M. (1960), Rings of Continuous Functions (Van Nostrand, Princeton).CrossRefGoogle Scholar
Grätzer, G. (1971), Lattice Theory (Freeman and Co., San Francisco).Google Scholar
Speed, T. P. (1973), “On rings of sets II. Zero-sets”, J. Austral. Math. Soc. 18, 185–199.CrossRefGoogle Scholar
Walker, R. C. (1974), The Stone-Čech Compactification (Springer-Verlag, New York).CrossRefGoogle Scholar