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Mansfield and Solovay type results on covering plane sets by lines

Published online by Cambridge University Press:  22 January 2016

Hiroshi P. Fujita
Hiroshi P. Fujita*
Affiliation:
Department of Mathematics, School of Science Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
*
Department of Mathematics, Faculty of Science Ehime University, Matsuyama 790, Japan
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F. van Engelen, K. Kunen, and A. W. Miller proved, in [EKM], that for every analytic set A on the plane, either A can be covered by a countable family of lines or else there is a perfect subset P of A such that no three points of P are collinear. In this paper, we present some generalizations of their result. In particular, a question which was raised by van Engelen et al. in the last paragraph of [EKM] is answered (see Section 3).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 145 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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