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• [2] I. Gelfand and A. N. Kolmogoroff, On rings of continuous functions on topological spaces, C.R. (Doklady) Acad. Sci. URSS vol. 22 (1939) pp. 11-15.
• [3] L. Gillman, M. Henriksen, and M. Jerison, On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions, Proc. Amer. Math. Soc. 5 (1954), 447–455. MR 0066627, https://doi.org/10.1090/S0002-9939-1954-0066627-6
• [4] L. J. Heider, Directed limits on rings of continuous functions, Duke Math. J. 23 (1956), 293–296. MR 0077106
• [5] Melvin Henriksen, On the equivalence of the ring, lattice, and semigroup of continuous functions, Proc. Amer. Math. Soc. 7 (1956), 959–960. MR 0082490, https://doi.org/10.1090/S0002-9939-1956-0082490-3
• [6] Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 0026239, https://doi.org/10.1090/S0002-9947-1948-0026239-9
• [7] Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 0020715, https://doi.org/10.1090/S0002-9904-1947-08856-X
• [8] A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. 16 (1940), 377–383. MR 0029476
• [9] R. S. Pierce, Coverings of a topological space, Trans. Amer. Math. Soc. 77 (1954), 281–298. MR 0070149, https://doi.org/10.1090/S0002-9947-1954-0070149-0
• [10] Lyle E. Pursell, An algebraic characterization of fixed ideals in certain function rings, Pacific J. Math. 5 (1955), 963–969. MR 0083478
• [11] Taira Shirota, A generalization of a theorem of I. Kaplansky, Osaka Math. J. 4 (1952), 121–132. MR 0052760
• [12] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, https://doi.org/10.1090/S0002-9947-1937-1501905-7

Bibliography

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F. W. Anderson, A lattice characterization of completely regular spaces, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 757-765. MR 0072451 (17:287a)

[2]

I. Gelfand and A. N. Kolmogoroff, On rings of continuous functions on topological spaces, C.R. (Doklady) Acad. Sci. URSS vol. 22 (1939) pp. 11-15.

[3]

L. Gillman, M. Henriksen, and M. Jerison, On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions, Proc. Amer. Math. Soc vol. 5 (1954) pp. 447-455. MR 0066627 (16:607h)

[4]

L. J. Heider, Directed limits on rings of continuous functions, Duke Math. J. vol. 23 (1956) pp. 293-296. MR 0077106 (17:990d)

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M. Henriksen, On the equivalence of the ring, lattice and semigroup of continuous functions, Proc. Amer. Math. Soc. vol. 7 (1956) pp. 959-960. MR 0082490 (18:559a)

[6]

E. Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 45-99. MR 0026239 (10:126e)

[7]

I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. vol 53 (1947) pp. 617-623. MR 0020715 (8:587e)

[8]

A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. vol. 16 (1949) pp. 377-383. MR 0029476 (10:612a)

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R. Pierce, Coverings of a topological space, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 281-289. MR 0070149 (16:1138e)

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L. E. Pursell, An algebraic characterization of fixed ideals in certain function rings, Pacific J. Math. Supplement II (1955) pp. 963-971. MR 0083478 (18:714e)

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T. Shirota, A generalization of a theorem of I. Kaplansky, Osaka Mathematical Journal vol. 4 (1952) pp. 121-132. MR 0052760 (14:669b)

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M. H. Stone, Applications of the theory of Boolean rings in general topology, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905