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Journal of the London Mathematical Society 1982 s2-26(3):531-540; doi:10.1112/jlms/s2-26.3.531
© 1982 by London Mathematical Society
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© Oxford University Press

Difference Spectra of Ideals for Non-Metrizable Groups

D. L. Salinger and J. D. Stegeman

School of Mathematics, Leeds University Leeds LS2 9JT
Mathematisch Instituut, Rijksuniversiteit Utrecht 3508 TA Utrecht, The Netherlands

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.


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