Topological Transformation Groups (Dover Books on Mathematics)

An advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem.
The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups.

Deane Montgomery (1909–92) received his Ph.D. from the University of Iowa, taught at Smith College from 1935–46, and was at the Institute for Advanced Study in Princeton from 1947 until his retirement in 1980. He was President of the American Mathematical Society in 1961–62.
Leo Zippin (1905–95) received his Ph.D. from the University of Pennsylvania.  He taught at Queens College in New York from 1938 until his retirement in 1971.