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An irreducible non-convex region

Published online by Cambridge University Press:  24 October 2008

Kathleen Ollerenshaw  and
L. J. Mordell
Kathleen Ollerenshaw
Affiliation:
11 Elm RoadManchester 20
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Extract

Some years ago I showed ((4), § 6, pp. 88–91) that the star domain K defined by the inequalities

has the minimum determinant Δ(K) = 2 and has an infinity of singular critical lattices. In this note I show that there is a unique irreducible star domain . That ís to say, there is just one star domain H contained in but different from K for which Δ(H) = Δ(K) = 2, and such that Δ(H′) < 2 for every star domain H′ contained in but different from H.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 194 - 200
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

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