Geodesic
Pointwise Sequentially Closed Ideals in C*(X)
Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 115-117

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to determine the conditions under which the maximal ideals of the ring C *(X)—the bounded real-valued continuous functions on a completely regular Hausdorff space X—are closed under pointwise convergence of sequences. Whereas the maximal ideals of C*(X) are closed under pointwise convergence of nets if and only if X is compact, it is shown that a necessary and sufficient condition for their pointwise sequential closure is that X be pseudocompact (i.e. that all real-valued continuous functions of X be bounded). 
Wilson, Richard G. Pointwise Sequentially Closed Ideals in C*(X). Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 115-117. doi: 10.4153/CMB-1973-022-5
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[1] 1. Dudley, R.M., On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483–507. Google Scholar

[2] 2. Gillman, L., and Jerison, M., Rings of continuous functions, Van Nostrand, Princeton, N.J., 1960. Google Scholar

[3] 3. Lorch, E.R., Compactifications, Baire functions, and Daniell integration, Acta Sci. Math. (Szeged) 24 (1963), 204–218. Google Scholar

[4] 4. Meyer, P.R., The Baire order problem for compact spaces, Duke Math. J. 33 (1966), 33–40. Google Scholar

[5] 5. Meyer, P.R., Topologies with the Stone-Weierstrass property, Trans. Amer. Math. Soc. 126 (1967), 236–243. Google Scholar

[6] 6. Stone, M.H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375–481. Google Scholar

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