On a question concerning countably generated $z$-ideals of $C(X)$
HTML articles powered by AMS MathViewer
- by Attilio Le Donne PDF
- Proc. Amer. Math. Soc. 80 (1980), 505-510 Request permission
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
- Rudolphe Bkouche, Pureté, mollesse et paracompacité, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1653–A1655 (French). MR 286803
- J. Glenn Brookshear, Projective ideals in rings of continuous functions, Pacific J. Math. 71 (1977), no. 2, 313–333. MR 454908, DOI 10.2140/pjm.1977.71.313
- 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).
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2
Additional 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