Closed countably generated structures in $C(X)$
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- by B. Roth
- Trans. Amer. Math. Soc. 177 (1973), 191-197
- DOI: https://doi.org/10.1090/S0002-9947-1973-0317027-9
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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
- Leonard Gillman, Countably generated ideals in rings of continuous functions, Proc. Amer. Math. Soc. 11 (1960), 660–666. MR 156189, DOI 10.1090/S0002-9939-1960-0156189-X 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.
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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