A subcategory of TOP
Authors:
Alan Dow and Stephen Watson
Journal:
Trans. Amer. Math. Soc. 337 (1993), 825837
MSC:
Primary 54A35; Secondary 18B30, 54B30
MathSciNet review:
1097165
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Abstract: We consider the smallest class of topological spaces which contains the converging sequence and which is closed under the operations of taking arbitrary sums, quotients and finite products. We show that if there is a model of settheory in which there is a measurable cardinal then there is a model in which this class does not contain all topological spaces. In addition, we prove that it is consistent that this class does contain all topological spacesin fact much more, a large cardinal is needed to produce a model of set theory in which this class is proper.
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 A. V. Arhangelskii, The spectrum of frequencies of a topological space and the classifications of spaces, Dokl. Akad. Nauk SSSR 206 (1972), 265268. MR 0394575 (52:15376)
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 Alan Dow, Istvan Juhasz, and William Weiss, Integervalued functions and increasing unions of first countable spaces, Israel J. Math. 67 (1989), 181192. MR 1026562 (90j:03092)
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 R. Engelking, General topology, PWNPolish Scientific Publishers, 1977. MR 0500780 (58:18316b)
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 W. G. Fleissner, The normal Moore space conjecture and large cardinals, Handbook of Set Theoretic Topology, NorthHolland, 1984, pp. 733760. MR 776635 (86m:54023)
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 David H. Fremlin, Measure algebras, Handbook of Boolean Algebras, vol. 3, NorthHolland, 1989, pp. 877980. MR 991611
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 Horst Herrlich, Categorical topology 19711981, General Topology and its Relations to Modern Analysis and Algebra (J. Novak, ed.), HeldermannVerlag, Belin, 1982, pp. 279383. MR 698425 (84d:54016)
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 M. Husek, Special classes of compact spaces, Proceedings of the Berlin Conference on Categorical Topology (Berlin, 1978), Lecture Notes in Math., vol. 719, SpringerVerlag, 1979. MR 544642 (80j:54018)
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 R. B. Jensen, The fine structure of the constructible hierarchy, Ann. of Math. Logic 4 (1972), 229308. MR 0309729 (46:8834)
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 V. I. Malyhin, On the tightness and the Suslin number of and of a product of spaces, Soviet Math. Dokl. 4 (1972), 496499.
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 R. M. Solovay, Realvalued measurable cardinals, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 397428. MR 0290961 (45:55)
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 A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690700. MR 0087078 (19:299b)
 [12]
 S. Todorcevic, My fans, May 1989, preprint.
 [13]
 , My new fan, May 1989, preprint.
 [14]
 , Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261294. MR 908147 (88i:04002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199310971659
PII:
S 00029947(1993)10971659
Article copyright:
© Copyright 1993
American Mathematical Society
