Note on the question of Sikora

Abstract

A natural topology on the set of left orderings on free abelian groups and free groups [Formula: see text], [Formula: see text] has studied in [A. S. Sikora, Topology on the spaces of orderings of groups, Bull. London Math. Soc. 36(4) (2004) 519–526; L. Smith, On ordering free groups, J. Symbolic Comput. 40 (2005) 1285–1290, Corrigendum (with A. Clay) 44 (2009) 1529–1532]. It has been proven already that in the abelian case the resulted topological space is a Cantor set. There was a conjecture: this is also true for the free group [Formula: see text] with [Formula: see text] generators. We point out the paper dealing with equivalent questions.