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The topology of free topological groups. (Russian. English summary) Zbl 1068.22002
Fundam. Prikl. Mat. 9, No. 2, 99-204 (2003); translation in J. Math. Sci., New York 131, No. 4, 5765-5838 (2005).
This paper deals with the notion of the free topological group \(F(X)\) in the sense of Markov and with the topological Abelian group \(A(X)\) which is generated by a Tikhonov space \(X\). A variety of results is presented to demonstrate how useful explicit descriptions of the topologies on these groups are. Moreover, a plenty of interesting examples is given to illustrate the use of such descriptions in many topological problems. In addition, several approaches to describe topologies on free topological groups are presented. This paper is worth to be read by any mathematician working with the notion of free topological group.

22A05 Structure of general topological groups
54H11 Topological groups (topological aspects)