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On a question concerning countably generated $ z$-ideals of $ C(X)$


Author: Attilio Le Donne
Journal: Proc. Amer. Math. Soc. 80 (1980), 505-510
MSC: Primary 54B17; Secondary 54D35, 54D60
DOI: https://doi.org/10.1090/S0002-9939-1980-0581015-7
MathSciNet review: 581015
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Abstract: In [D$ _{1}$] the following question was asked: is every countably generated z-ideal of $ C(X)$ of the form $ {O^A} = \bigcap\nolimits_{p \in A} {{O^p}} $, for some zero-set A of $ \beta X$? It is proved here that the answer is affirmative when X is normal and first countable; and an example is given, disproving the general conjecture. For terminology and notation see [GJ], [D$ _{1}$].


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DOI: https://doi.org/10.1090/S0002-9939-1980-0581015-7
Article copyright: © Copyright 1980 American Mathematical Society