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Difference Spectra of Ideals for Non‐Metrizable Groups
Author(s) -
Salinger D. L.,
Stegeman J. D.
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-26.3.531
Subject(s) - metrization theorem , abelian group , mathematics , locally compact space , ideal (ethics) , pure mathematics , spectrum (functional analysis) , group (periodic table) , closed set , elementary abelian group , discrete mathematics , physics , mathematical analysis , separable space , epistemology , quantum mechanics , philosophy
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 .