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

Frolík, Zdeněk

doi:10.1090/S0002-9939-1971-0270337-X

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

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

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

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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.

References

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