A subcategory of TOP
HTML articles powered by AMS MathViewer
- by Alan Dow and Stephen Watson PDF
- Trans. Amer. Math. Soc. 337 (1993), 825-837 Request permission
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
- A. V. Arhangel′skiĭ, Frequency spectrum of a topological space and classification of spaces, Dokl. Akad. Nauk SSSR 206 (1972), 265–268 (Russian). MR 0394575
- Alan Dow, István Juhász, and William Weiss, Integer-valued functions and increasing unions of first countable spaces, Israel J. Math. 67 (1989), no. 2, 181–192. MR 1026562, DOI 10.1007/BF02937294
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- William G. Fleissner, The normal Moore space conjecture and large cardinals, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 733–760. MR 776635
- David H. Fremlin, Measure algebras, Handbook of Boolean algebras, Vol. 3, North-Holland, Amsterdam, 1989, pp. 877–980. MR 991611
- H. Herrlich, Categorical topology 1971–1981, General topology and its relations to modern analysis and algebra, V (Prague, 1981) Sigma Ser. Pure Math., vol. 3, Heldermann, Berlin, 1983, pp. 279–383. MR 698425
- M. Hušek, Special classes of compact spaces, Categorical topology (Proc. Internat. Conf., Free Univ. Berlin, Berlin, 1978) Lecture Notes in Math., vol. 719, Springer, Berlin, 1979, pp. 167–175. MR 544642
- R. Björn Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229–308; erratum, ibid. 4 (1972), 443. With a section by Jack Silver. MR 309729, DOI 10.1016/0003-4843(72)90001-0 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.
- Robert M. Solovay, Real-valued measurable cardinals, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR 0290961
- A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, DOI 10.1090/S0002-9939-1956-0087078-6 S. Todorcevic, My fans, May 1989, preprint. —, My new fan, May 1989, preprint.
- Stevo Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), no. 3-4, 261–294. MR 908147, DOI 10.1007/BF02392561
Additional Information
- © Copyright 1993 American Mathematical Society
- 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