03291nam a22004815i 4500 978-3-031-58513-5 DE-He213 20251030112248.0 cr nn 008mamaa 240601s2024 sz | s |||| 0|eng d 9783031585135 978-3-031-58513-5 10.1007/978-3-031-58513-5 doi QA611-614.97 PBP bicssc MAT038000 bisacsh PBP thema López, Rafael. author. (orcid)0000-0003-3108-7009 https://orcid.org/0000-0003-3108-7009 aut http://id.loc.gov/vocabulary/relators/aut 78020 Point-Set Topology [electronic resource] : A Working Textbook / by Rafael López. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. VIII, 398 p. 120 illus., 7 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Undergraduate Mathematics Series, 2197-4144 - Introduction -- Topological spaces -- Proximity on a topological space -- Metric spaces -- Continuity -- Homeomorphisms and topological invariants -- Product topology -- Connectedness -- Compactness -- Quotient topology -- The fundamental group. This 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. Topology. 72917 Topology. 72917 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031585128 Printed edition: 9783031585142 Springer Undergraduate Mathematics Series, 2197-4144 75368 https://doi.org/10.1007/978-3-031-58513-5 ZDB-2-SMA ZDB-2-SXMS 60382 60382