LEADER 03017nam 22004935 450 001 9910865252603321 005 20251008171002.0 010 $a9783031585135$b(electronic bk.) 010 $z9783031585128 024 7 $a10.1007/978-3-031-58513-5 035 $a(MiAaPQ)EBC31359958 035 $a(Au-PeEL)EBL31359958 035 $a(CKB)32213458300041 035 $a(MiAaPQ)EBC31361391 035 $a(Au-PeEL)EBL31361391 035 $a(DE-He213)978-3-031-58513-5 035 $a(EXLCZ)9932213458300041 100 $a20240601d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPoint-Set Topology $eA Working Textbook /$fby Rafael López 205 $a1st ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (397 pages) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 311 08$aPrint version: López, Rafael Point-Set Topology Cham : Springer International Publishing AG,c2024 9783031585128 327 $a- Introduction -- Topological spaces -- Proximity on a topological space -- Metric spaces -- Continuity -- Homeomorphisms and topological invariants -- Product topology -- Connectedness -- Compactness -- Quotient topology -- The fundamental group. 330 $aThis textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus. 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aTopology 606 $aTopology 615 0$aTopology. 615 14$aTopology. 676 $a514 700 $aLopez$b Rafael$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910865252603321 996 $aPoint-Set Topology$94168678 997 $aUNINA