Dikranjan, Dikran N.; Stoyanov, Luchezar N.; Prodanov, Ivan R. Topological groups. Characters, dualities, and minimal group topologies. (English) Zbl 0687.22001 Pure and Applied Mathematics, 130. New York etc.: Marcel Dekker, Inc. x, 287 p. $ 99.75 (US and Canada); $ 119.50 (All other countries) (1990). This excellent book arises from almost twenty years investigations of minimal group topologies due to the authors. An accessory output of the work is a new approach to the existence of continuous characters, the Haar integral, the Pontryagin duality. The book contains 7 chapters. 1. Existence of characters. 2. Applications of the Følner theorem. 3. Pontryagin duality. 4. Quasi-torsion elements in topological groups. 5. Minimal abelian groups. 6. Minimality of products of topological abelian groups. 7. Minimal and totally minimal nonabelian groups. Many information and recent results are included in end-of-chapter exercises with hints for most of them. Chapter summaries, historical remarks, open problems and a extensive list of references are prepared for a reader. Reviewer: Yu.N.Mukhin Cited in 3 ReviewsCited in 88 Documents MSC: 22-02 Research exposition (monographs, survey articles) pertaining to topological groups 22A05 Structure of general topological groups 22B05 General properties and structure of LCA groups Keywords:minimal group topologies; continuous characters; Haar integral; Pontryagin duality; Følner theorem; topological abelian groups PDFBibTeX XMLCite \textit{D. N. Dikranjan} et al., Topological groups. Characters, dualities, and minimal group topologies. New York etc.: Marcel Dekker, Inc. (1990; Zbl 0687.22001)