Selected Publication:
Kuba, G.
(2021):
ON DECOMPOSITIONS OF THE REAL LINE
COLLOQ MATHWARSAW. 2021; 165(2): 241252.
FullText
FullText_BOKU
 Abstract:
 Let Xt be a totally disconnected subset of R for each t is an element of R. We construct a partition {Yt vertical bar t is an element of R} of R into nowhere dense Lebesgue null sets Yt such that for every t is an element of R there exists an increasing homeomorphism from Xt onto Yt. 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
Altmetric: