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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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##### References:
 [1] Gul’ko, Proc. Baku Intern. Topol. Conf 193 (1987) [2] Graev, Amer. Math. Soc. Transl 8 pp 305– (1962) [3] DOI: 10.1112/jlms/s2-10.4.431 · Zbl 0304.22003 · doi:10.1112/jlms/s2-10.4.431 [4] DOI: 10.2307/2040178 · Zbl 0278.22001 · doi:10.2307/2040178 [5] Pestov, Soviet Math. Dokl 26 pp 380– (1982) [6] DOI: 10.1007/BFb0065191 · doi:10.1007/BFb0065191 [7] Morris, Categorical Topology pp 375– (1983) [8] Markov, Doklady Akad. Nauk 31 pp 299– (1941) [9] Markov, Amer. Math. Soc. Transl 30 pp 11– (1950) [10] Katz, Math. Proc. Camb. Philos. Soc 100 pp 347– (1986) [11] DOI: 10.1093/qmath/35.2.173 · Zbl 0556.22001 · doi:10.1093/qmath/35.2.173 [12] DOI: 10.1112/jlms/s2-12.2.199 · Zbl 0318.22002 · doi:10.1112/jlms/s2-12.2.199
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