Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1971-0270337-X
MathSciNet review: 0270337
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. Čech, Topological spaces, 2nd ed., Publ. House Czech. Acad. Sci., Prague, 1965; English transl, of 1st ed., Wiley, New York, 1966. MR 35 #2254. MR 0211373 (35:2254)
  • [2] Z. Frolík, A measurable map with analytic domain and metrizable range is quotient, Bull. Amer. Math. Soc. 76 (1970), 1112-1117. MR 0265539 (42:448)
  • [3] -, A survey of descriptive theory of sets and spaces, Czechoslovak Math. J. 20 (1970), 406-167. MR 0266757 (42:1660)
  • [4] 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. 157-173. MR 26 #3002. MR 0145471 (26:3002)
  • [5] A. W. Hager, Approximation of real continuous functions on Lindelöf spaces, Proc. Amer. Math. Soc. 22 (1969), 156-163. MR 39 #6062. MR 0244748 (39:6062)
  • [6] A. W. Hager and D. G. Johnson, A note on certain subalgebras of $ C(X)$, Canad. J. Math. 20 (1968), 389-393. MR 36 #5697. MR 0222647 (36:5697)
  • [7] E. Hewitt, Certain generalizations of the Weierslrass approximation theorem, Duke Math. J. 14(1947), 410-427. MR 9, 95. MR 0021662 (9:95e)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.40

Retrieve articles in all journals with MSC: 54.40


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

American Mathematical Society