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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (72) -n.3 (73), 2013/

On free groups in classes of groups with topologies

Authors: Mitrofan M. Choban, Liubomir L. Chiriac

Abstract

We study properties of free groups in distinct classes of groups with topologies. The conditions under which the quasi-metric on the space of generators X is extended to an invariant quasi-metric on a free group F(X, V) in the fixed quasi-variety V of groups with topologies are given. This result is applied to the study:
- of free paratopological groups;
- of free quasitopological groups;
- of free semitopological groups;
- of free left topological groups.

Department of Mathematics
Tiraspol State University
MD-2069, Chisinau
Moldova
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