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Mapping a set of reals onto the reals

  • Arnold W. Miller (a1)
Abstract
Abstract

In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω1.

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[1]Bagemihl F. and Sprinkle H., On a proposition of Sierpinski's which is equivalent to the continuum hypothesis, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 726728.
[2]Baumgartner J. and Laver R., Iterated perfect set forcing, Annals of Mathematical Logic, vol. 17 (1979), pp. 271288.
[3]Isbell J., Spaces without large projective subspaces, Mathematica Scandinarica, vol. 17 (1965), pp. 89105.
[4]Isbell J., A set whose square can map onto a perfect set, Proceedings of the American Mathematical Society, vol. 20 (1969), pp. 254255.
[5]Kunen K., Doctoral Dissertation, Stanford University, 1968.
[6]Kuratowski K., Topology, vol. 1, Academic Press, New York, 1966.
[7]Laver R., On the consistency of Borel's conjecture. Acta Mathematica, vol. 137 (1976), pp. 151169.
[8]Royden H.L., Real analysis, Macmillan, New York, 1968.
[9]Sierpinski W., Sur un ensemble non dénombrable donte toute image continue est de mesure null, Fundamenta Mathematical, vol. 11 (1928), p. 304.
[10]Sierpinski W., Hypothèse du continu, Monografie Matematyczne, Tom IV, Warsaw, 1934.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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