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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stone-Weierstrass theorems for $ C(X)$ with the sequential topology


Author: Zdeněk Frolík
Journal: Proc. Amer. Math. Soc. 27 (1971), 486-494
MSC: Primary 54.40
MathSciNet review: 0270337
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Abstract: The spaces $ P$ with one of the following two properties are studied: every continuous function is a Baire function with respect to any algebra $ \mathcal{R}$ of continuous functions such that $ \mathcal{R}$ projectively generates the topology, or with respect to any algebra which distinguishes the points. The former property is equivalent to the statement that of any pair of disjoint zero sets at least one is Lindelöf, the latter implies that the space is Lindelöf and is implied by analyticity. Connections with the Blackwell problem are shown.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0270337-X
PII: S 0002-9939(1971)0270337-X
Keywords: Lindelöf, almost Lindelöf, Baire-minimal, Blackwell space, analytic, algebra of continuous functions, Baire set, Baire function, sequential topology
Article copyright: © Copyright 1971 American Mathematical Society