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Difference-covers that are not k-sum-covers. II

Published online by Cambridge University Press:  24 October 2008

D. M. Connolly  and
J. H. Williamson
D. M. Connolly
Affiliation:
University of York†
J. H. Williamson
Affiliation:
University of York†
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Abstract

We examine the possibility of establishing the existence of a compact subset E of ℝ such that E–E contains a non-degenerate interval and the semigroup generated by E has measure zero. We show that the existence of such an E is equivalent to the existence of a sequence of difference-covers that are not k-sum-covers for each k∈ℕ, and, further, is equivalent to the existence of an asymmetric maximal Raikov system.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 63 - 73
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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