Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube

?This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span. For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam’s conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach