Topological groups for topologists. I (Q1977159)

The author gives a survey of the theory of topological groups, with regard to topological properties, and classes of topological groups defined by such properties. A second part of the survey has already appeared [ibid. 6, No. 1, 1-41 (2000)]. The paper under review treats basic properties (separation, metrizability, subgroups and quotients, locally compact groups, direct products, thin subsets, and comparable topologies), then completions and sequentially complete groups, and finally to embeddability questions. A wealth of results is presented, with references to recent literature. As it is to be expected with a survey like this, no proofs are given.