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Open subgroups of free abelian topological groups. (English) Zbl 0802.22001
The authors prove that open subgroups of free Markov (Graev) abelian topological groups are free Markov (Graev) abelian topological groups. This result implies that if \(A\) is a free topological abelian group, \(B\) an open subgroup and \(X,Y\) are free topological bases for \(A\) and \(B\) respectively, then \(\dim X = \dim Y\).
MSC:
22A05 Structure of general topological groups
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