On zero-dimensionality of subgroups of locally compact groups
Shakhmatov, Dmitriĭ B.
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 581-582 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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 $G$.

Publié le : 1991-01-01
Classification:  22A05,  22D05,  54D45,  54F45,  54H11,  54H99 
@article{118435,
     author = {Dmitri\u\i\ B. Shakhmatov},
     title = {On zero-dimensionality of subgroups of locally compact groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {581-582},
     zbl = {0746.22004},
     mrnumber = {1159803},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118435}
}

Shakhmatov, Dmitriĭ B. On zero-dimensionality of subgroups of locally compact groups. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 581-582. http://gdmltest.u-ga.fr/item/118435/

Engelking R. General Topology, Warszawa, PWN, 1977. | MR 0500780 | Zbl 0684.54001

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

Shakhmatov D.B. Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204. (1990) | MR 1068169 | Zbl 0709.22001

Tkačenko M.G. Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) | MR 1093863