Nonequality of Dimensions for Metric Groups
General Topology
2007-05-23 v1 Group Theory
Abstract
An embeddability criterion for zero-dimensional metrizable topological spaces in zero-dimensional metrizable topological groups is given. A space which can be embedded as a closed subspace in a zero-dimensional metrizable group but is not strongly zero-dimensional is constructed; thereby, an example of a metrizable group with noncoinciding dimensions ind and dim is obtained. It is proved that one of Kulesza's zero-dimensional metrizable spaces cannot be embedded in a metrizable zero-dimensional group.
Keywords
Cite
@article{arxiv.math/0606146,
title = {Nonequality of Dimensions for Metric Groups},
author = {Ol'ga V. Sipacheva},
journal= {arXiv preprint arXiv:math/0606146},
year = {2007}
}