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Nonequality of Dimensions for Metric Groups

Research paper by Ol'ga V. Sipacheva

Indexed on: 07 Jun '06Published on: 07 Jun '06Published in: Mathematics - General Topology



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.