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Topological invariants in algebraic environment. (English) Zbl 1030.54026
Hušek, Miroslav (ed.) et al., Recent progress in general topology II. Based on the Prague topological symposium, Prague, Czech Republic, August 19-25, 2001. Amsterdam: Elsevier. 1-57 (2002).
This is a very well written survey of results on topological algebra covering the eleven year span 1990-2001, by one of the best specialists in the area. Among the subjects covered one can find cardinal invariants, separate and joint continuity of the group operation, extremal disconnectedness and similar properties, free topological groups, completions of topological groups, Bohr topologies and duality of topological Abelian groups.
As the paper is a survey, no proofs are given, maybe a few sketches. But on the other hand the comments are very illuminating. The list of references is as complete as possible so that any person interested in a particular subject can obtain more information.
Over sixty open problems and their history and importance are discussed. As the author points out, the survey, a gargantuan task, does not touch every single possible development and it is definitely influenced by the author’s personal interests. Nevertheless, it is a solid recount of “what’s going on” in this area.
For the entire collection see [Zbl 1005.00037].

54H11 Topological groups (topological aspects)
54-02 Research exposition (monographs, survey articles) pertaining to general topology
22A99 Topological and differentiable algebraic systems