| 020 | $a9783031308864$9978-3-031-30886-4 |
| 082 | $a515.42$223 |
| 099 | $aOnline resource: Springer |
| 100 | $aJung, Soon-Mo.$eauthor.$4aut$4http://id.loc.gov/vocabulary/relators/aut |
| 245 | $aUlam’s Conjecture on Invariance of Measure in the Hilbert Cube$hEBook /$cby Soon-Mo Jung. |
| 250 | $a1st ed. 2023. |
| 260 | $aCham :$bSpringer Nature Switzerland :$bImprint: Birkhäuser,$c2023. |
| 300 | $aX, 190 p. 2 illus.$bonline resource. |
| 336 | $atext$btxt$2rdacontent |
| 337 | $acomputer$bc$2rdamedia |
| 338 | $aonline resource$bcr$2rdacarrier |
| 440 | $aFrontiers in Mathematics,$x1660-8054 |
| 505 | $aPreface -- 1. Topology -- 2. Hilbert spaces -- 3. Measure theory -- 4. Extension of isometries -- 5. History of Ulam’s conjecture -- 6. Ulam’s conjecture. - Bibliography -- Index. |
| 520 | $aThis 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 space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam’s conjecture; the conjecture is fully proved in Chapter 6. |
| 533 | $a Digital reproduction.- |
| 533 | $b Cham : |
| 533 | $c Springer International Publishing, |
| 533 | $d 2023. - |
| 533 | $nMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| 538 | $aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| 710 | $aSpringerLink (Online service) |
| 830 | $aFrontiers in Mathematics,$x1660-8054 |
| 856 | $uhttps://doi.org/10.1007/978-3-031-30886-4 |
