Some open questions on topological groups (Q2762064)

The authors comment on some recent results and problems for most part related to the Bohr topology of an arbitrary topological group. Though the subject relates closely to topological algebra, it leads quickly and naturally to questions of interest to researchers working in a variety of disciplines. They consider also the Pontryagin-van Kampen duality theory of topological abelian groups and the extension of this theory to nonabelian groups introduced by Chu. The rich collection of well explained problems should be very valuable to people interested in the theory of topological groups.NEWLINENEWLINENEWLINEThe following is an up-date status of the problems communicated to this reviewer by the authors. (1) Questions 7.1, 7.2 and 7.3 have been answered negatively by Ahbarov and Shavgulidze, also by Hernández and Trigos-Arrieta independently. The results of the last two authors is in the article ``Polar reflexive spaces vs Pontryagin duality'' (preprint in Topology Atlas). (2) Question 3.6 was answered by \textit{J. Galindo} and \textit{S. Hernández} in their article ``Interpolation sets and Bohr topology of locally compact groups'' (preprint).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00016].