Concerning rings of continuous functions. (English) Zbl 0058.10003
Keywords:
functional analysisReferences:
| [1] | Richard F. Arens and Irving Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948), 457 – 481. · Zbl 0032.00702 |
| [2] | Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823 – 844. · Zbl 0017.42803 · doi:10.2307/1968839 |
| [3] | Jean Dieudonné, Une généralisation des espaces compacts, J. Math. Pures Appl. (9) 23 (1944), 65 – 76 (French). · Zbl 0060.39508 |
| [4] | C. H. Dowker, On countably paracompact spaces, Canadian J. Math. 3 (1951), 219 – 224. · Zbl 0042.41007 |
| [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. · Zbl 0056.10803 |
| [6] | F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen, Math. Ann. 65 (1908), no. 4, 435 – 505 (German). · JFM 39.0099.01 · doi: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. · Zbl 0052.34101 |
| [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. · Zbl 0051.34001 |
| [10] | Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45 – 99. · Zbl 0032.28603 |
| [11] | Edwin Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161 – 189. · Zbl 0040.06401 |
| [12] | Irving Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153 – 183. · Zbl 0034.16604 · doi:10.2307/2371662 |
| [13] | M. Katětov, Measures in fully normal spaces, Fund. Math. 38 (1951), 73 – 84. · Zbl 0045.17101 |
| [14] | C. Kuratowski, Topologie I, Warsaw, 1933. · JFM 59.0563.02 |
| [15] | S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942. · Zbl 0061.39302 |
| [16] | Neal H. McCoy, Rings and ideals, Carus Monograph Series, no. 8, The Open Court Publishing Company, LaSalle, Ill., 1948. · Zbl 0041.36406 |
| [17] | Bedřich Pospíšil, Remark on bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 845 – 846. · Zbl 0017.42901 · doi:10.2307/1968840 |
| [18] | Taira Shirota, A class of topological spaces, Osaka Math. J. 4 (1952), 23 – 40. · Zbl 0047.41704 |
| [19] | Roman Sikorski, Remarks on some topological spaces of high power, Fund. Math. 37 (1950), 125 – 136. · Zbl 0041.09705 |
| [20] | A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977 – 982. · Zbl 0032.31403 |
| [21] | M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375 – 481. · Zbl 0017.13502 |
| [22] | A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math. vol. 30 (1938) pp. 68-89. · Zbl 0018.34702 |
| [23] | -, Drei Überdeckungssätze der allgemeinen Mengenlehre, Fund. Math. vol. 30 (1938) pp. 132-155. · JFM 64.0034.01 |
| [24] | A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), no. 1, 544 – 561 (German). · JFM 55.0963.01 · doi:10.1007/BF01782364 |
| [25] | S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. vol. 16 (1930) pp. 140-150. · JFM 56.0920.04 |
| [26] | B. L. van der Waerden, Moderne Algebra, Berlin, 1940. · Zbl 0022.29801 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
