Results 241 to 250 of about 291,341 (280)

The Topology of Free Topological Groups

Journal of Mathematical Sciences, 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.
exaly   +3 more sources

Subgroups of Free Topological Groups and Free Topological Products of Topological Groups

Journal of the London Mathematical Society, 1975
Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9].
Brown, R., Hardy, J. P. L.
openaire   +1 more source

On The Profinite Topology on a Free Group

Bulletin of the London Mathematical Society, 1993
The profinite topology on a free group \(F\) is generated by the subgroups of finite index and their cosets. M. Hall jun. showed that each finitely generated subgroup is closed. J.-E. Pin and the reviewer conjectured that each product \(H_ 1 H_ 2 \dots H_ n\), where each \(H_ i\) is a finitely generated subgroup, is closed.
Ribes, Luis, Zalesskij, Pavel A.
openaire   +2 more sources

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