Stroppel M. Locally Compact Groups

European Mathematical Society, 2006. — 313 p. — (EMS Textbooks in Mathematics) — ISBN: 3037190167This book introduces the reader to the theory of locally compact groups, leading from the basics about topological groups to more involved topics, including transformation groups, the Haar integral, and Pontryagin duality. I have also included several applications to the structure theory of locally compact Abelian groups, to topological rings and fields. The presentation is rounded off by a chapter on topological semigroups, paying special respect to results that identify topological groups inside this wider class. In order to show the results from Pontryagin theory at work, I have also included the determination of those locally compact Abelian groups that are homogeneous in the sense that their automorphism group acts transitively on the set of non-trivial elements. A crucial but deep tool for any deeper understanding of locally compact groups is the approximation by Lie groups. The chapter on Hilbert’s fifth problem gives an overview. The chart following this preface gives a rough impression of the logical dependence between the sections.Preliminaries
Topological Groups
Topological Transformation Groups
The Haar Integral
Categories of Topological Groups
Locally Compact Abelian Groups
Locally Compact Semigroups
Hilbert’s Fifth Problem