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Marczewski sets, measure and the Baire property. II


Author: John T. Walsh
Journal: Proc. Amer. Math. Soc. 106 (1989), 1027-1030
MSC: Primary 28A05; Secondary 26A21, 54H05
DOI: https://doi.org/10.1090/S0002-9939-1989-0967489-6
MathSciNet review: 967489
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Abstract: An example is given (in ZFC) of a hereditarily Marczewski set which does not have the Baire property in the wise sense and is not Lebesgue measurable. It is then shown that Marczewski sets, which do not satisfy the c.c.c., possess a hull property.


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  • [1] J. B. Brown and G. V. Cox, Classical theory of totally imperfect spaces, Real Anal. Exchange 7 (1981/82), no. 2, 185–232. MR 657320
  • [2] 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
  • [3] John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443
  • [4] W. Sierpiński, Sur un problèm concernant les familles d'ensembles parfaits, Fund. Math. 31 (1938), 1-3.
  • [5] E. Szpilrajn-Marczewski, Sur certains invariants de l'opération (A), Fund. Math. 21 (1933), 229-235.
  • [6] -, Sur une classe de fonctions de M. Sierpinski et la classe correspondante d'ensembles, Fund. Math. 24 (1935), 17-34.
  • [7] John Thomas Walsh, Marczewski sets, measure and the Baire property, Fund. Math. 129 (1988), no. 2, 83–89. MR 959434, https://doi.org/10.4064/fm-129-2-83-89

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0967489-6
Keywords: Marczewski sets, Baire property, measurability, continuum hypothesis, operation $ (A)$, c.c.c., hull
Article copyright: © Copyright 1989 American Mathematical Society

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