Stone-Weierstrass theorems for with the sequential topology

Author:
Zdeněk Frolík

Journal:
Proc. Amer. Math. Soc. **27** (1971), 486-494

MSC:
Primary 54.40

DOI:
https://doi.org/10.1090/S0002-9939-1971-0270337-X

MathSciNet review:
0270337

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Abstract | References | Similar Articles | Additional Information

Abstract: The spaces with one of the following two properties are studied: every continuous function is a Baire function with respect to any algebra of continuous functions such that 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0270337-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