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Selected Publication:

Kuba, G.
(2021): ON DECOMPOSITIONS OF THE REAL LINE
COLLOQ MATH-WARSAW. 2021; 165(2): 241-252. FullText FullText_BOKU

Abstract:
Let X-t be a totally disconnected subset of R for each t is an element of R. We construct a partition {Y-t vertical bar t is an element of R} of R into nowhere dense Lebesgue null sets Y-t such that for every t is an element of R there exists an increasing homeomorphism from X-t onto Y-t. In particular, the real line can be partitioned into 2(N0) Cantor sets and also into 2(N0) mutually nonhomeomorphic compact subspaces. Furthermore we prove that for every cardinal number kappa with 2 <= kappa <= 2(N0) the real line (as well as the Baire space R \ Q) can be partitioned into exactly kappa homeomorphic Bernstein sets and also into exactly kappa mutually nonhomeomorphic Bernstein sets. We also investigate partitions of R into Marczewski sets, including the possibility that they are Luzin sets or Sierphiski sets.
Authors BOKU Wien:
Kuba Gerald
BOKU Gendermonitor:


Find related publications in this database (Keywords)
topology of the line
subspaces
decompositions


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