On a question concerning countably generated $z$-ideals of $C(X)$
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- by Attilio Le Donne
- Proc. Amer. Math. Soc. 80 (1980), 505-510
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581015-7
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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$_{1}$].References
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- G. De Marco, On the countably generated $z$-ideals of $C(X)$, Proc. Amer. Math. Soc. 31 (1972), 574–576. MR 288563, DOI 10.1090/S0002-9939-1972-0288563-3 —, Projectivity of pure ideals (to appear).
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Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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