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On sequences of lattice packings

Published online by Cambridge University Press:  17 April 2009

Joseph Hammer
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
Denis Dwyer
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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Abstract

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In this note we establish theorems on compactness of lattice packings.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Blaschke, Wilhelm, “Kreis und Kugel”, Jber. Deutsch. Math.-Verein. 24 (1915), 195207.Google Scholar
[2]Groemer, H., “Continuity properties of Voronoi domains”, Monatsh. Math. 75 (1971), 423431.CrossRefGoogle Scholar
[3]Lekkerkerker, C.G., Geometry of numbers (Bibliotheca Mathematica, 8. Wolters-Noordhoff, Groningen; Horth-Holland, Amsterdam, London; 1969).Google Scholar
[4]Mahler, K., “On lattice points in n–dimensional star bodies. I. Existence theorems”, Proc. Roy. Soc. London Ber. A 187 (1946), 151187.Google Scholar
[5]Mahler, K., “On the critical lattices of arbitrary point sets”, Canad. J. Math. 1 (1949), 7887.CrossRefGoogle Scholar
[6]Melzak, Z.A., “A class of star-shaped bodies”, Canad. Math. Bull. 2 (1959), 175180.CrossRefGoogle Scholar
[7]Rudin, Walter, Functional analysis (McGraw-Hill, New York, St. Louis, San Francisco, Düsseldorf, Johannesburg, Kuala Lumpur, London, Mexico, Montreal, New Delhi, Panama, Rio de Janeiro, Singapore, Sydney, Toronto, 1973).Google Scholar