Consistent solution of Markov's problem about algebraic sets

2006/05/20 by Ol'ga V. Sipacheva, Sipacheva, Ol'ga V.
Mathematics · #22A05 (Primary) #54H11 (Secondary) #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #math.GN #math.GR #msc:22A05 #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0605558

Version 2: The proof is made much more detailed. Several misprints are corrected

arxiv created 2007/04/07 · arxiv updated 2009/12/01

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.

Related

• Markov's problem for free groups
• Unconditionally tau-Closed and tau-Algebraic Sets in Groups
• A Class of Groups in Which All Unconditionally Closed Sets are Algebraic
• An alternative foundation and the generalized continuum hypothesis
• A generalization of the Open Mapping Theorem and a possible generalization of the Baire Category Theorem