TY - JOUR

T1 - Note on the question of Sikora

AU - Storozhuk, Konstantin

PY - 2018/3

Y1 - 2018/3

N2 - A natural topology on the set of left orderings on free abelian groups and free groups (Formula presented.), (Formula presented.) 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 presented.) with (Formula presented.) generators. We point out the paper dealing with equivalent questions.

AB - A natural topology on the set of left orderings on free abelian groups and free groups (Formula presented.), (Formula presented.) 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 presented.) with (Formula presented.) generators. We point out the paper dealing with equivalent questions.

KW - Ordered group

KW - SPACE

KW - LATTICE-ORDERED GROUPS

UR - http://www.scopus.com/inward/record.url?scp=85044193874&partnerID=8YFLogxK

U2 - 10.1142/S0218216518400084

DO - 10.1142/S0218216518400084

M3 - Article

AN - SCOPUS:85044193874

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 3

M1 - 1840008

ER -