A history of topological and analytical semigroups. A personal view
It does not seem feasible to summarize the author's excellent treatment of the history of topological and analytical semigroups. This reviewer will therefore indicate some of the highlights of the paper and add a small amount of insight of his own. This paper presents a very well conceived historical perspective of the development of topological and analytical semigroups and the researchers that made contributions to this development. The chronology presented at the conclusion of the paper is outstanding. In his 1955 AMS address (referenced in this paper), A. D. Wallace stated that he was reporting on a large number of small theorems, which indicates that topological semigroups theory was in its early stages of discovery. The author points out that an early important discovery of Wallace was the structure of the minimal ideal of a compact semigroup. He also brings to light some of the earlier results of well-known mathematicians that contributed to this and other important facets of the theory. The 1966 AMS address delivered by P. S. Mostert reported on a small number of large theorems, which indicated that substantial depth was being developed in compact semigroup theory. Structure theorems were being discovered by researchers such as Hofmann and Mostert, Koch, Lawson, and their colleagues. D. R. Brown, along with his students and colleagues, later made substantial contributions to the theory of compact divisible semigroups. Through the work of Keimel and others, this theory provided a bridge to Lie semigroup theory. In more recent times (as indicated by the author), the frontier of Lie semigroup theory has been extended. The primary contributors here are Hofmann, Lawson, and their colleagues.
scientific article; zbMATH DE number 1491097