LEADER 04416nam 2200637Ia 450 001 9910830329303321 005 20170815153743.0 010 $a1-283-30615-8 010 $a9786613306159 010 $a1-118-03158-X 010 $a1-118-03058-3 035 $a(CKB)2550000000056585 035 $a(EBL)708227 035 $a(OCoLC)778616733 035 $a(SSID)ssj0000555648 035 $a(PQKBManifestationID)11388296 035 $a(PQKBTitleCode)TC0000555648 035 $a(PQKBWorkID)10533617 035 $a(PQKB)11275056 035 $a(MiAaPQ)EBC708227 035 $a(PPN)204506387 035 $a(EXLCZ)992550000000056585 100 $a20060921d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTopology$b[electronic resource] $epoint-set and geometric /$fPaul L. Shick 210 $aHoboken, N.J. $cWiley-Interscience$dc2007 215 $a1 online resource (291 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 $a0-470-09605-5 320 $aIncludes bibliographical references (p. 263-264) and index. 327 $aTopology: Point-Set and Geometric; CONTENTS; Foreword; Acknowledgments; 1 Introduction: Intuitive Topology; 1.1 Introduction: Intuitive Topology; 2 Background on Sets and Functions; 2.1 Sets; 2.2 Functions; 2.3 Equivalence Relations; 2.4 Induction; 2.5 Cardinal Numbers; 2.6 Groups; 3 Topological Spaces; 3.1 Introduction; 3.2 Definitions and Examples; 3.3 Basics on Open and Closed Sets; 3.4 The Subspace Topology; 3.5 Continuous Functions; 4 More on Open and Closed Sets and Continuous Functions; 4.1 Introduction; 4.2 Basis for a Topology; 4.3 Limit Points; 4.4 Interior, Boundary and Closure 327 $a4.5 More on Continuity5 New Spaces from Old; 5.1 Introduction; 5.2 Product Spaces; 5.3 Infinite Product Spaces (Optional); 5.4 Quotient Spaces; 5.5 Unions and Wedges; 6 Connected Spaces; 6.1 Introduction; 6.2 Definition, Examples and Properties; 6.3 Connectedness in the Real Line; 6.4 Path-connectedness; 6.5 Connectedness of Unions and Finite Products; 6.6 Connectedness of Infinite Products (Optional); 7 Compact Spaces; 7.1 Introduction; 7.2 Definition, Examples and Properties; 7.3 Hausdorff Spaces and Compactness; 7.4 Compactness in the Real Line; 7.5 Compactness of Products 327 $a7.6 Finite Intersection Property (Optional)8 Separation Axioms; 8.1 Introduction; 8.2 Definition and Examples; 8.3 Regular and Normal spaces; 8.4 Separation Axioms and Compactness; 9 Metric Spaces; 9.1 Introduction; 9.2 Definition and Examples; 9.3 Properties of Metric Spaces; 9.4 Basics on Sequences; 10 The Classification of Surfaces; 10.1 Introduction; 10.2 Surfaces and Higher-Dimensional Manifolds; 10.3 Connected Sums of Surfaces; 10.4 The Classification Theorem; 10.5 Triangulations of Surfaces; 10.6 Proof of the Classification Theorem; 10.7 Euler Characteristics and Uniqueness 327 $a11 Fundamental Groups and Covering Spaces11.1 Introduction; 11.2 Homotopy of Functions and Paths; 11.3 An Operation on Paths; 11.4 The Fundamental Group; 11.5 Covering Spaces; 11.6 Fundamental Group of the Circle and Related Spaces; 11.7 The Fundamental Groups of Surfaces; References; Index 330 $aThe essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics-connected and pa 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aAlgebraic topology 606 $aPoint set theory 615 0$aAlgebraic topology. 615 0$aPoint set theory. 676 $a514 676 $a514.2 676 $a514/.2 700 $aShick$b Paul Louis$f1956-$01615743 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830329303321 996 $aTopology$93946076 997 $aUNINA