LEADER 04887nam 2200889 a 450 001 9910790493803321 005 20230801223628.0 010 $a1-283-85794-4 010 $a3-11-027734-4 024 7 $a10.1515/9783110277333 035 $a(CKB)2670000000211132 035 $a(EBL)893992 035 $a(OCoLC)796384299 035 $a(SSID)ssj0000696963 035 $a(PQKBManifestationID)11363611 035 $a(OCoLC)780161503 035 $a(PQKBTitleCode)TC0000696963 035 $a(PQKBWorkID)10689992 035 $a(PQKB)10860232 035 $a(PQKBManifestationID)16204953 035 $a(PQKB)21458823 035 $a(MiAaPQ)EBC893992 035 $a(DE-B1597)175111 035 $a(OCoLC)797050569 035 $a(DE-B1597)9783110277333 035 $a(Au-PeEL)EBL893992 035 $a(CaPaEBR)ebr10582196 035 $a(CaONFJC)MIL417044 035 $a(EXLCZ)992670000000211132 100 $a20120312d2012 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acz 200 10$aTopological analysis$b[electronic resource] $efrom the basics to the triple degree for nonlinear Fredholm inclusions /$fMartin Va?th 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (500 p.) 225 1 $aDe Gruyter series in nonlinear analysis and applications,$x0941-813X ;$v16 300 $aDescription based upon print version of record. 311 0 $a3-11-027733-6 311 0 $a3-11-027722-0 320 $aIncludes bibliographical references and indexes. 327 $tFront matter --$tPreface --$tContents --$tChapter 1. Introduction --$tPart I. Topology and Multivalued Maps --$tChapter 2. Multivalued Maps --$tChapter 3. Metric Spaces --$tChapter 4. Spaces Defined by Extensions, Retractions, or Homotopies --$tChapter 5. Advanced Topological Tools --$tPart II. Coincidence Degree for Fredholm Maps --$tChapter 6. Some Functional Analysis --$tChapter 7. Orientation of Families of Linear Fredholm Operators --$tChapter 8. Some Nonlinear Analysis --$tChapter 9. The Brouwer Degree --$tChapter 10. The Benevieri-Furi Degrees --$tPart III. Degree Theory for Function Triples --$tChapter 11. Function Triples --$tChapter 12. The Degree for Finite-Dimensional Fredholm Triples --$tChapter 13. The Degree for Compact Fredholm Triples --$tChapter 14. The Degree for Noncompact Fredholm Triples --$tBibliography --$tIndex of Symbols --$tIndex 330 $aThis monograph aims to give a self-contained introduction into the whole field of topological analysis: Requiring essentially only basic knowledge of elementary calculus and linear algebra, it provides all required background from topology, analysis, linear and nonlinear functional analysis, and multivalued maps, containing even basic topics like separation axioms, inverse and implicit function theorems, the Hahn-Banach theorem, Banach manifolds, or the most important concepts of continuity of multivalued maps. Thus, it can be used as additional material in basic courses on such topics. The main intention, however, is to provide also additional information on some fine points which are usually not discussed in such introductory courses. The selection of the topics is mainly motivated by the requirements for degree theory which is presented in various variants, starting from the elementary Brouwer degree (in Euclidean spaces and on manifolds) with several of its famous classical consequences, up to a general degree theory for function triples which applies for a large class of problems in a natural manner. Although it has been known to specialists that, in principle, such a general degree theory must exist, this is the first monograph in which the corresponding theory is developed in detail. 410 0$aDe Gruyter series in nonlinear analysis and applications ;$v16. 606 $aTopological degree 606 $aTopological spaces 606 $aFredholm operators 606 $aAlgebraic topology 610 $aAnalysis. 610 $aBanach Manifold. 610 $aFredholm. 610 $aHahn-Banach Theorem. 610 $aImplicit Function Theorem. 610 $aInverse Function Theorem. 610 $aLinear Functional Analysis. 610 $aMultivalued Map. 610 $aNonlinear Functional Analysis. 610 $aNonlinear Inclusion. 610 $aSeparation Axiom. 610 $aTopology. 610 $aTriple Degree. 615 0$aTopological degree. 615 0$aTopological spaces. 615 0$aFredholm operators. 615 0$aAlgebraic topology. 676 $a515/.724 686 $aSK 620$2rvk 700 $aVa?th$b Martin$f1967-$061875 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910790493803321 996 $aTopological analysis$93720655 997 $aUNINA