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Cofinal families of compacta in separable metric spaces


Author: Fons van Engelen
Journal: Proc. Amer. Math. Soc. 104 (1988), 1271-1273
MSC: Primary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1988-0969060-8
MathSciNet review: 969060
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Abstract: We show that if $ X$ is a $ \Pi _1^1$-set, then the family of compact subsets of $ X$ contains a cofinal (w.r.t. inclusion) subset of cardinality $ {\mathbf{d}}$; the same is true if $ X$ is $ \Pi _3^1$, under strong set-theoretic hypotheses.


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  • [1] Eric K. van Douwen, The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111–167. MR 776622
  • [2] A. J. M. van Engelen, Homogeneous zero-dimensional absolute Borel sets, CWI Tract, vol. 27, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1986. MR 851765
  • [3] Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna. Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
    Ryszard Engelking, General topology, PWN—Polish Scientific Publishers, Warsaw, 1977. Translated from the Polish by the author; Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. MR 0500780
  • [4] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [5] N. Luzin and W. Sierpiñski, Sur quelques propriétés des ensembles (A), Bull. Int. Acad. Sci. Cracovie Série A Sci. Math, (1918), 35-48.
  • [6] Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
  • [7] John R. Steel, Analytic sets and Borel isomorphisms, Fund. Math. 108 (1980), no. 2, 83–88. MR 594307

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DOI: https://doi.org/10.1090/S0002-9939-1988-0969060-8
Article copyright: © Copyright 1988 American Mathematical Society