Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A subcategory of TOP


Authors: Alan Dow and Stephen Watson
Journal: Trans. Amer. Math. Soc. 337 (1993), 825-837
MSC: Primary 54A35; Secondary 18B30, 54B30
DOI: https://doi.org/10.1090/S0002-9947-1993-1097165-9
MathSciNet review: 1097165
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 set-theory 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 spaces--in fact much more, a large cardinal is needed to produce a model of set theory in which this class is proper.


References [Enhancements On Off] (What's this?)

  • [1] A. V. Arhangelskii, The spectrum of frequencies of a topological space and the classifications of spaces, Dokl. Akad. Nauk SSSR 206 (1972), 265-268. MR 0394575 (52:15376)
  • [2] Alan Dow, Istvan Juhasz, and William Weiss, Integer-valued functions and increasing unions of first countable spaces, Israel J. Math. 67 (1989), 181-192. MR 1026562 (90j:03092)
  • [3] R. Engelking, General topology, PWN-Polish Scientific Publishers, 1977. MR 0500780 (58:18316b)
  • [4] W. G. Fleissner, The normal Moore space conjecture and large cardinals, Handbook of Set Theoretic Topology, North-Holland, 1984, pp. 733-760. MR 776635 (86m:54023)
  • [5] David H. Fremlin, Measure algebras, Handbook of Boolean Algebras, vol. 3, North-Holland, 1989, pp. 877-980. MR 991611
  • [6] Horst Herrlich, Categorical topology 1971-1981, General Topology and its Relations to Modern Analysis and Algebra (J. Novak, ed.), Heldermann-Verlag, Belin, 1982, pp. 279-383. MR 698425 (84d:54016)
  • [7] M. Husek, Special classes of compact spaces, Proceedings of the Berlin Conference on Categorical Topology (Berlin, 1978), Lecture Notes in Math., vol. 719, Springer-Verlag, 1979. MR 544642 (80j:54018)
  • [8] R. B. Jensen, The fine structure of the constructible hierarchy, Ann. of Math. Logic 4 (1972), 229-308. MR 0309729 (46:8834)
  • [9] V. I. Malyhin, On the tightness and the Suslin number of $ \exp X$ and of a product of spaces, Soviet Math. Dokl. 4 (1972), 496-499.
  • [10] R. M. Solovay, Real-valued measurable cardinals, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 397-428. MR 0290961 (45:55)
  • [11] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690-700. 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), 261-294. MR 908147 (88i:04002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54A35, 18B30, 54B30

Retrieve articles in all journals with MSC: 54A35, 18B30, 54B30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1097165-9
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society