Consistent solution of Markov's problem about algebraic sets
Abstract
It is proved that the continuum hypothesis implies the existence of a group M containing a nonalgebraic unconditionally closed set, i.e., a set which is closed in any Hausdorff group topology on M but is not an intersection of finite unions of solution sets of equations in M.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2006
 arXiv:
 arXiv:math/0605558
 Bibcode:
 2006math......5558S
 Keywords:

 Mathematics  Group Theory;
 Mathematics  General Topology;
 22A05 (Primary);
 54H11 (Secondary)
 EPrint:
 Version 2: The proof is made much more detailed. Several misprints are corrected