On zero-dimensionality of subgroups of locally compact groups

Dmitriĭ B. Shakhmatov

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 3, page 581-582
  • ISSN: 0010-2628

Abstract

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Improving the recent result of the author we show that ind H = 0 is equivalent to dim H = 0 for every subgroup H of a Hausdorff locally compact group G .

How to cite

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Shakhmatov, 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

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  1. Engelking R., General Topology, Warszawa, PWN, 1977. Zbl0684.54001MR0500780
  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. Zbl0416.43001MR0156915
  3. Shakhmatov D.B., Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204. (1990) Zbl0709.22001MR1068169
  4. Tkačenko M.G., Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) MR1093863

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