• [1] Richard F. Arens and Irving Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948), 457–481. MR 0025453, 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 0013297
• [4] C. H. Dowker, On countably paracompact spaces, Canadian J. Math. 3 (1951), 219–224. MR 0043446
• [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 0066627, 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 0059479
• [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 0055664, 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 0026239, 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 0042684, https://doi.org/10.4064/fm-37-1-161-189
• [12] Irving Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153–183. MR 0019596, https://doi.org/10.2307/2371662
• [13] M. Katětov, Measures in fully normal spaces, Fund. Math. 38 (1951), 73–84. MR 0048531, 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 0050872
• [19] Roman Sikorski, Remarks on some topological spaces of high power, Fund. Math. 37 (1950), 125–136. MR 0040643, 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 0026802, 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.

Bibliography

[1]

R. Arens and I. Kaplansky, Topological representations of algebras, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 457-481. MR 0025453 (10:7c)

[2]

E. Čech, On bicompact spaces, Ann. of Math. vol. 38 (1937) pp. 823-844. MR 1503374

[3]

J. Dieudonné, Une généralisation des espaces compacts, J. Math. Pures Appl. vol. 23 (1944) pp. 65-76. MR 0013297 (7:134f)

[4]

C. H. Dowker, On countably compact spaces, Canadian Journal of Mathematics vol. 3 (1951) pp. 219-224. MR 0043446 (13:264c)

[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. vol. 5 (1954) pp. 447-455. MR 0066627 (16:607h)

[6]

F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen, Math. Ann. vol. 65 (1908) pp. 435-505. MR 1511478

[7]

-, Grundzüge der Mengenlehre, Leipzig, 1914.

[8]

M. Henriksen, On the prime ideals of the ring of entire functions, Pacific Journal of Mathematics vol. 3 (1953) pp. 711-720. MR 0059479 (15:537c)

[9]

M. Henriksen and J. R. Isbell, On the continuity of the real roots of an algebraic equation, Proc. Amer. Math. Soc. vol. 4 (1953) pp. 431-434. MR 0055664 (14:1107e)

[10]

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

[11]

-, Linear functionals on spaces of continuous functions, Fund. Math. vol. 37 (1950) pp. 161-189. MR 0042684 (13:147g)

[12]

I. Kaplansky, Topological rings, Amer. J. Math. vol. 69 (1947) pp. 153-183. MR 0019596 (8:434b)

[13]

M. Katětov, Measures in fully normal spaces, Fund Math. vol. 38 (1951) pp. 73-84. MR 0048531 (14:27c)

[14]

C. Kuratowski, Topologie I, Warsaw, 1933.

[15]

S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942.

[16]

N. H. McCoy, Rings and ideals, Mathematical Association of America, 1948. MR 0026038 (10:96b)

[17]

B. Pospíšil, Remark on bicompact spaces, Ann. of Math. vol. 38 (1937) pp. 845-846. MR 1503375

[18]

T. Shirota, A class of topological spaces, Osaka Math. J. vol. 4 (1952) pp. 23-40. MR 0050872 (14:395b)

[19]

R. Sikorski, Remarks on some topological spaces of high power, Fund. Math. vol. 37 (1950) pp. 125-136. MR 0040643 (12:727e)

[20]

A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 977-982. MR 0026802 (10:204c)

[21]

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

[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. vol. 102 (1930) pp. 544-561. MR 1512595

[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.