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Article

Shakhmatov, Dmitrii B.
On zero-dimensionality of subgroups of locally compact groups. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 32 (1991), issue 3, pp. 581-582
MSC: 22A05, 22D05, 54D45, 54F45, 54H11, 54H99 | MR 1159803 | Zbl 0746.22004
Keywords:
zero-dimensionality; covering dimension; inductive dimension; subgroup; locally compact group
Summary:
Improving the recent result of the author we show that $\operatorname{ind}H=0$ is equivalent to $\operatorname{dim} H=0$ for every subgroup $H$ of a Hausdorff locally compact group $G$.
References:
[1] Engelking R.: General Topology. Warszawa, PWN, 1977. MR 0500780 | Zbl 0684.54001
[2] Hewitt E., Ross K.A.: Abstract Harmonic Analysis, vol. 1. Structure of Topological Groups. Integration Theory. Group Representations. Die Grundlehren der mathematischen Wissenshaften, Bd. 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915 | Zbl 0416.43001
[3] Shakhmatov D.B.: Imbeddings into topological groups preserving dimensions. Topology Appl. 36 (1990), 181-204. MR 1068169 | Zbl 0709.22001
[4] Tkačenko M.G.: Factorization theorems for topological groups and their applications. Topology Appl. 38 (1991), 21-37. MR 1093863
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