02951nam a22003975i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100014500224245009000369250001800459264007500477300006600552336002600618337002600644338003600670347002400706490005800730505025200788520124901040650001402289650001402303710003402317773002602351776003602377776003602413830005802449856004602507978-3-031-58513-5DE-He21320251030112248.0cr nn 008mamaa240601s2024    sz |    s    |||| 0|eng d  a97830315851357 a10.1007/978-3-031-58513-52doi 4aQA611-614.97 7aPBP2bicssc 7aMAT0380002bisacsh 7aPBP2thema1 aLópez, Rafael.eauthor.0(orcid)0000-0003-3108-70091https://orcid.org/0000-0003-3108-70094aut4http://id.loc.gov/vocabulary/relators/aut10aPoint-Set Topologyh[electronic resource] :bA Working Textbook /cby Rafael López.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aVIII, 398 p. 120 illus., 7 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Undergraduate Mathematics Series,x2197-41440 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.  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. 0aTopology.14aTopology.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303158512808iPrinted edition:z9783031585142 0aSpringer Undergraduate Mathematics Series,x2197-414440uhttps://doi.org/10.1007/978-3-031-58513-5