Topological groups.

*(English)*Zbl 0604.22002
Handbook of set-theoretic topology, 1143-1263 (1984).

[For the entire collection see Zbl 0546.00022.]

This paper is in the nature of a survey, but contains proofs of several of the assertions that are formulated. It is addressed to those interested in topological aspects of the theory of topological groups. All the results are accompanied by detailed historical references. There is an extensive bibliography, reflecting the state of the questions considered and going up to the most recent period. It contains about 280 titles.

The contents of the paper are as follows: (1) Introduction: Seven major results; (2) Topological pathology; (3) Cardinal invariants; (4) Measurability conditions and the group Hom(G, \({\mathbb{T}})\); (5) Topological groups with special topological properties; (6) Pseudocompact topological groups; (7) Dense subgroups with special properties; (8) Products of topological groups; (9) Topologizing a group; (10) Not all homogeneous spaces are topological groups; (11) Concluding remarks and acknowledgements.

This paper is in the nature of a survey, but contains proofs of several of the assertions that are formulated. It is addressed to those interested in topological aspects of the theory of topological groups. All the results are accompanied by detailed historical references. There is an extensive bibliography, reflecting the state of the questions considered and going up to the most recent period. It contains about 280 titles.

The contents of the paper are as follows: (1) Introduction: Seven major results; (2) Topological pathology; (3) Cardinal invariants; (4) Measurability conditions and the group Hom(G, \({\mathbb{T}})\); (5) Topological groups with special topological properties; (6) Pseudocompact topological groups; (7) Dense subgroups with special properties; (8) Products of topological groups; (9) Topologizing a group; (10) Not all homogeneous spaces are topological groups; (11) Concluding remarks and acknowledgements.

##### MSC:

22A05 | Structure of general topological groups |

54H13 | Topological fields, rings, etc. (topological aspects) |

22-02 | Research exposition (monographs, survey articles) pertaining to topological groups |