LEADER 03366nam 22005295 450 001 9911011655403321 005 20250625125921.0 010 $a9783031910111 024 7 $a10.1007/978-3-031-91011-1 035 $a(CKB)39449849500041 035 $a(MiAaPQ)EBC32175860 035 $a(Au-PeEL)EBL32175860 035 $a(DE-He213)978-3-031-91011-1 035 $a(OCoLC)1525502261 035 $a(EXLCZ)9939449849500041 100 $a20250625d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aContinuum Theory /$fby Alejandro Illanes 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (536 pages) 225 1 $aUniversitext,$x2191-6675 311 08$a9783031910104 327 $aChapter 1. Introduction -- Chapter 2. Locally Connected Continua -- Chapter 3. CuttingWires and Bumping Boundaries -- Chapter 4. Indecomposable Continua -- Chapter 5. Characterizing Arcs and Circles -- Chapter 6. Finite Graphs -- Chapter 7. Dendroids -- Chapter 8. The Cantor Set -- Chapter 9. Hyperspaces of Continua -- Chapter 10. Models of Hyperspaces -- Chapter 11. Irreducible Continua -- Chapter 12. Unicoherence -- Chapter 13. The Fixed Point Property -- Chapter 14. Inverse Limits -- Chapter 15. Homogeneity of the Hilbert Cube -- Chapter 16. Absolute Retracts -- Chapter 17. Stronger Properties of the Pseudo-Arc. 330 $aThis graduate textbook provides a natural and structured introduction to Continuum Theory, guiding readers from fundamental concepts to advanced topics. It covers classical results such as locally connected continua, indecomposable continua, arcs, circles, finite graphs, dendroids, and the relationship between the Cantor set and continua. The second half explores the theory of hyperspaces, presenting various models, their properties, and key theorems, while also highlighting elegant and lesser-known mathematical results. Designed for readers with an understanding of basic topology, this book serves as a valuable resource for PhD students and researchers in mathematics. It offers a rigorous and thorough approach, with detailed proofs that clarify complex arguments?especially regarding the intricate properties of the pseudo-arc. A wealth of exercises helps reinforce understanding and develop problem-solving skills. This book stands out for its depth and breadth, covering a range of topics. It provides a comprehensive study of hyperspace models, the homogeneity of the Hilbert cube, and the pseudo-arc, offering one of the few accessible and complete proofs of its unique properties. With its structured progression and careful exposition, this book is a valuable reference for anyone interested in continuum theory. 410 0$aUniversitext,$x2191-6675 606 $aTopology 606 $aMathematical analysis 606 $aTopology 606 $aAnalysis 615 0$aTopology. 615 0$aMathematical analysis. 615 14$aTopology. 615 24$aAnalysis. 676 $a514 700 $aIllanes$b Alejandro$066082 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911011655403321 996 $aContinuum Theory$94400572 997 $aUNINA