StoneWeierstrass theorems for with the sequential topology
Author:
Zdeněk Frolík
Journal:
Proc. Amer. Math. Soc. 27 (1971), 486494
MSC:
Primary 54.40
MathSciNet review:
0270337
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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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 Z. Frolík, A measurable map with analytic domain and metrizable range is quotient, Bull. Amer. Math. Soc. 76 (1970), 11121117. MR 0265539 (42:448)
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 , A survey of descriptive theory of sets and spaces, Czechoslovak Math. J. 20 (1970), 406167. MR 0266757 (42:1660)
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 Z. Frolík, A contribution to the descriptive theory of sets and spaces, Proc. Sympos. General Topology and its Relations to Modern Analysis and Algebra (Prague, 1961), Academic Press, New York; Publ. House Czech. Acad. Sci., Prague, 1962, pp. 157173. MR 26 #3002. MR 0145471 (26:3002)
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 A. W. Hager, Approximation of real continuous functions on Lindelöf spaces, Proc. Amer. Math. Soc. 22 (1969), 156163. MR 39 #6062. MR 0244748 (39:6062)
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 A. W. Hager and D. G. Johnson, A note on certain subalgebras of , Canad. J. Math. 20 (1968), 389393. MR 36 #5697. MR 0222647 (36:5697)
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 E. Hewitt, Certain generalizations of the Weierslrass approximation theorem, Duke Math. J. 14(1947), 410427. MR 9, 95. MR 0021662 (9:95e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919710270337X
PII:
S 00029939(1971)0270337X
Keywords:
Lindelöf,
almost Lindelöf,
Baireminimal,
Blackwell space,
analytic,
algebra of continuous functions,
Baire set,
Baire function,
sequential topology
Article copyright:
© Copyright 1971
American Mathematical Society
