Homogeneous subsets of the real line

نویسنده

  • Jan Van Mill
چکیده

If A C R then A is homogeneous provided that A + Q = A. As an application we give an elementary proof of Menu’s theorem that the real line can be decomposed in two homogeneous homeomorphic subsets. We also show that such a decomposition is not topologically unique. There are homogeneous A, B C R with A RBA, B ~ RBB but A B.

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تاریخ انتشار 2006