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LEADER: 04671cam a2200409 a 4500
001 5986978
005 20221121220816.0
008 060413t20062006njua b 001 0 eng
010 $a 2006046178
020 $a9780471687559 (cloth : alk. paper)
020 $a0471687553 (cloth : alk. paper)
024 $a99820392610
035 $a(OCoLC)ocm67361774\
035 $a(NNC)5986978
035 $a(OCoLC)67361774
035 $a5986978
040 $aDLC$cDLC$dBAKER$dUKM$dC#P$dYUS$dBTCTA$dYDXCP$dCOO$dUUS$dNOR
042 $apcc
050 00 $aQA611$b.B275 2006
082 00 $a514$222
100 1 $aBasener, William F.,$d1973-$0http://id.loc.gov/authorities/names/n2006028965
245 10 $aTopology and its applications /$cWilliam F. Basener.
260 $aHoboken, N.J. :$bWiley-Interscience,$c[2006], ©2006.
300 $axxxvii, 339 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aPure and applied mathematics
504 $aIncludes bibliographical references (p. 333-336) and index.
505 00 $tPreface --$tIntroduction --$g1.1.$tPreliminaries --$g1.2.$tCardinality --$g1.$tContinuity --$g1.1.$tContinuity and open sets in R n --$g1.2.$tContinuity and open sets in topological spaces --$g1.3.$tMetric, product, and quotient topologies --$g1.4.$tSubsets of topological spaces --$g1.5.$tContinuous functions and topological equivalence --$g1.6.$tSurfaces --$g1.7.$tApplication : chaos in dynamical systems --$g1.7.1.$tHistory of chaos --$g1.7.2. A$tsimple example --$g1.7.3.$tNotions of chaos --$g2.$tCompactness --$g2.1.$tClosed bounded subsets of R --$g2.2.$tCompact spaces --$g2.3.$tIdentification spaces and compactness --$g2.4.$tConnectedness and path-connectedness --$g2.5.$tCantor sets --$g2.6.$tApplication : compact sets in population dynamics and fractals --$g3.$tManifolds and complexes --$g3.1.$tManifolds --$g3.2.$tTriangulations --$g3.3.$tClassification of surfaces --$g3.3.1.$tGluing disks --$g3.3.2.$tPlanar models --$g3.3.3.$tClassification of surfaces --$g3.4.$tEuler characteristic --$g3.5.$tTopological groups --$g3.6.$tGroup actions and orbit spaces --$g3.6.1.$tFlows on tori --$g3.7.1.$tRobotic coordination and configuration spaces --$g3.7.2.$tGeometry of manifolds --$g3.7.3. The$ttopology of the universe --
505 00 $g4.$tHomotopy and the winding number --$g4.1.$tHomotopy and paths --$g4.2. The$twinding number --$g4.3.$tDegrees of maps --$g4.4. The$tBrouwer fixed point theorem --$g4.5. The$tBorsuk-Ulam theorem --$g4.6.$tVector fields and the Poincaré index theorem --$g4.7.$tApplications 1 --$g4.7.1. The$tfundamental theorem of algebra --$g4.7.2.$tSandwiches --$g4.7.3.$tGame theory and Nash equilibria --$g4.8.$tApplications 2 : calculus --$g4.8.1.$tVector fields, path integrals, and the winding number --$g4.8.2.$tVector fields on surfaces --$g4.8.3.$tIndex theory for n-symmetry fields --$g4.9.$tIndex theory in computer graphics --$g5.$tFundamental group --$g5.1.$tDefinition and basic properties --$g5.2.$tHomotopy equivalence and retracts --$g5.3. The$tfundamental group of spheres and tori --$g5.4. The$tSeifert-van Kampen theorem --$g5.4.1.$tFlowers and surfaces --$g5.4.2. The$tSeifert-van Kampen theorem --$g5.5.$tCovering spaces --$g5.6.$tGroup actions and deck transformations --$g5.7.$tApplications --$g5.7.1.$tOrder and emergent patterns in condensed matter physics --
505 00 $g6.$tHomology --$g6.1.$t[triangle]-complexes --$g6.2.$tChains and boundaries --$g6.3.$tExamples and computations --$g6.4.$tSingular homology --$g6.5.$tHomotopy invariance --$g6.6.$tBrouwer fixed point theorem for D n --$g6.7.$tHomology and the fundamental group --$g6.8.$tBetti numbers and the Euler characteristic --$g6.9.$tComputational homology--$g6.9.1.$tComputing Betti numbers --$g6.9.2.$tBuilding a filtration --$g6.9.3.$tPersistent homology --$tAppendix A : Knot theory --$tAppendix B : Groups --$tAppendix C : Perspectives in topology --$gC.1.$tPoint set topology --$gC.2.$tGeometric topology --$gC.3.$tAlgebraic topology --$gC.4.$tCombinatorial topology --$gC.5.$tDifferential topology --$tReferences --$tBibliography--$tIndex.
650 0 $aTopology$vTextbooks.
830 0 $aPure and applied mathematics (John Wiley & Sons : Unnumbered)$0http://id.loc.gov/authorities/names/n42745140
856 42 $3Contributor biographical information$uhttp://www.loc.gov/catdir/enhancements/fy0740/2006046178-b.html
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy0740/2006046178-d.html
856 41 $3Table of contents only$uhttp://www.loc.gov/catdir/enhancements/fy0740/2006046178-t.html
852 00 $bmat$hQA611$i.B275 2006