Difference Spectra of Ideals for Non-Metrizable Groups

A set of non-synthesis is constructed in a non-metrizable compact abelian group in such a way that the set of non-synthesis points is not closed. It is further shown that such sets exist in every non-metrizable locally compact abelian group. In contrast, the spectrum of a closed ideal of A(G) is sho...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 1982-12, Vol.s2-26 (3), p.531-540
Main Authors: Salinger, D. L., Stegeman, J. D.
Format: Article
Language:English
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Summary:A set of non-synthesis is constructed in a non-metrizable compact abelian group in such a way that the set of non-synthesis points is not closed. It is further shown that such sets exist in every non-metrizable locally compact abelian group. In contrast, the spectrum of a closed ideal of A(G) is shown to be closed for every locally compact abelian group G.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/s2-26.3.531