论文标题
关于真实行的分解
On decompositions of the real line
论文作者
论文摘要
令X_T为R中的每个t的真实行R的完全断开子集。我们构造一个分区{y_t | t in r}进入无处浓密的lebesgue null设置y_t，使得r中的每个t都存在从x_t到y_t的同构越来越多。特别是，实际行可以分为2^{aleph_0} cantor集，也可以分为2^{aleph_0}相互非塑形紧凑型子空间。此外，我们证明，对于具有2 \ leq k \ leq 2^{Aleph_0}的每个基数K，可以将真实线（以及Baire Space r \ q）分开为恰好的K同型Bernstein套件，以及确切的K Muthormally非蜂窝状Bernstein sets。我们还将R分区调查为Marczewski集合，包括它们是Luzin Sets或Sierpinski集的可能性。
Let X_t be a totally disconnected subset of the real line R for each t in R. We construct a partition {Y_t | t in R} of R into nowhere dense Lebesgue null sets Y_t such that for every t in R there exists an increasing homeomorphism from X_t onto Y_t. In particular, the real line can be partitioned into 2^{aleph_0} Cantor sets and also into 2^{aleph_0} mutually non-homeomorphic compact subspaces. Furthermore we prove that for every cardinal number k with 2 \leq k \leq 2^{aleph_0} the real line (as well as the Baire space R\Q) can be partitioned into exactly k homeomorphic Bernstein sets and also into exactly k mutually non-homeomorphic Bernstein sets. We also investigate partitions of R into Marczewski sets, including the possibility that they are Luzin sets or Sierpinski sets.
