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Transactions of the American Mathematical Society

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Closed countably generated structures in $ C(X)$


Author: B. Roth
Journal: Trans. Amer. Math. Soc. 177 (1973), 191-197
MSC: Primary 46E25; Secondary 46E05
DOI: https://doi.org/10.1090/S0002-9947-1973-0317027-9
MathSciNet review: 0317027
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Abstract: Let $ C(X)$ be the space of continuous real or complex valued functions on a compact space X with the sup norm topology. In the present paper, the subalgebras, vector lattices, and vector lattice ideals of $ C(X)$ which are closed and countably generated are characterized.


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

  • [1] L. Gillman, Countably generated ideals in rings of continuous functions, Proc. Amer. Math. Soc. 11 (1960), 660-666. MR 27 #6120. MR 0156189 (27:6120)
  • [2] M. Stone, A generalized Weierstrass approximation theorem, Studies in Modern Analysis, Math. Assoc. of Amer. Studies in Math., vol. 1, Prentice-Hall, Englewood Cliffs, N. J., 1962.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0317027-9
Keywords: Spaces of continuous functions, subalgebras of continuous functions, vector lattices of continuous functions, countably generated subalgebras, countably generated vector lattices, countably generated vector lattice ideals
Article copyright: © Copyright 1973 American Mathematical Society

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