Concerning rings of continuous functions
Authors:
Leonard Gillman and Melvin Henriksen
Journal:
Trans. Amer. Math. Soc. 77 (1954), 340-362
MSC:
Primary 56.0X
DOI:
https://doi.org/10.1090/S0002-9947-1954-0063646-5
MathSciNet review:
0063646
Full-text PDF Free Access
References | Similar Articles | Additional Information
- [1] Richard F. Arens and Irving Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948), 457–481. MR 25453, https://doi.org/10.1090/S0002-9947-1948-0025453-6
- [2] Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823–844. MR 1503374, https://doi.org/10.2307/1968839
- [3] Jean Dieudonné, Une généralisation des espaces compacts, J. Math. Pures Appl. (9) 23 (1944), 65–76 (French). MR 13297
- [4] C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219–224. MR 43446, https://doi.org/10.4153/cjm-1951-026-2
- [5] 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 66627, https://doi.org/10.1090/S0002-9939-1954-0066627-6
- [6] F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen, Math. Ann. 65 (1908), no. 4, 435–505 (German). MR 1511478, https://doi.org/10.1007/BF01451165
- [7] -, Grundzüge der Mengenlehre, Leipzig, 1914.
- [8] Melvin Henriksen, On the prime ideals of the ring of entire functions, Pacific J. Math. 3 (1953), 711–720. MR 59479
- [9] Melvin Henriksen and J. R. Isbell, On the continuity of the real roots of an algebraic equation, Proc. Amer. Math. Soc. 4 (1953), 431–434. MR 55664, https://doi.org/10.1090/S0002-9939-1953-0055664-2
- [10] Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, https://doi.org/10.1090/S0002-9947-1948-0026239-9
- [11] Edwin Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161–189. MR 42684, https://doi.org/10.4064/fm-37-1-161-189
- [12] Irving Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153–183. MR 19596, https://doi.org/10.2307/2371662
- [13] M. Katětov, Measures in fully normal spaces, Fund. Math. 38 (1951), 73–84. MR 48531, https://doi.org/10.4064/fm-38-1-73-84
- [14] C. Kuratowski, Topologie I, Warsaw, 1933.
- [15] S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942.
- [16] Neal H. McCoy, Rings and ideals, Carus Monograph Series, no. 8, The Open Court Publishing Company, LaSalle, Ill., 1948. MR 0026038
- [17] Bedřich Pospíšil, Remark on bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 845–846. MR 1503375, https://doi.org/10.2307/1968840
- [18] Taira Shirota, A class of topological spaces, Osaka Math. J. 4 (1952), 23–40. MR 50872
- [19] Roman Sikorski, Remarks on some topological spaces of high power, Fund. Math. 37 (1950), 125–136. MR 40643, https://doi.org/10.4064/fm-37-1-125-136
- [20] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977–982. MR 26802, https://doi.org/10.1090/S0002-9904-1948-09118-2
- [21] 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
- [22] A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math. vol. 30 (1938) pp. 68-89.
- [23] -, Drei Überdeckungssätze der allgemeinen Mengenlehre, Fund. Math. vol. 30 (1938) pp. 132-155.
- [24] A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), no. 1, 544–561 (German). MR 1512595, https://doi.org/10.1007/BF01782364
- [25] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. vol. 16 (1930) pp. 140-150.
- [26] B. L. van der Waerden, Moderne Algebra, Berlin, 1940.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 56.0X
Retrieve articles in all journals with MSC: 56.0X
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1954-0063646-5
Article copyright:
© Copyright 1954
American Mathematical Society