On zero-dimensionality of subgroups of locally compact groups
Commentationes Mathematicae Universitatis Carolinae (1991)
- Volume: 32, Issue: 3, page 581-582
- ISSN: 0010-2628
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topShakhmatov, Dmitriĭ B.. "On zero-dimensionality of subgroups of locally compact groups." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 581-582. <http://eudml.org/doc/247314>.
@article{Shakhmatov1991,
abstract = {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 $G$.},
author = {Shakhmatov, Dmitriĭ B.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {zero-dimensionality; covering dimension; inductive dimension; subgroup; locally compact group; covering dimension; inductive dimension; subgroup; Hausdorff locally compact group},
language = {eng},
number = {3},
pages = {581-582},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On zero-dimensionality of subgroups of locally compact groups},
url = {http://eudml.org/doc/247314},
volume = {32},
year = {1991},
}
TY - JOUR
AU - Shakhmatov, Dmitriĭ B.
TI - On zero-dimensionality of subgroups of locally compact groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 3
SP - 581
EP - 582
AB - 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 $G$.
LA - eng
KW - zero-dimensionality; covering dimension; inductive dimension; subgroup; locally compact group; covering dimension; inductive dimension; subgroup; Hausdorff locally compact group
UR - http://eudml.org/doc/247314
ER -
References
top- Engelking R., General Topology, Warszawa, PWN, 1977. Zbl0684.54001MR0500780
- 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. Zbl0416.43001MR0156915
- Shakhmatov D.B., Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204. (1990) Zbl0709.22001MR1068169
- Tkačenko M.G., Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) MR1093863
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