Topological and approximation methods of degree theory of set-valued maps

Kryszewski, Wojciech

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Topological and approximation methods of degree theory of set-valued maps

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Wojciech Kryszewski

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Rozprawy Matematyczne tom/nr w serii: 336 wydano: 1994

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CONTENTS
   Introduction................................................................................................................5
   Preliminaries...............................................................................................................7
A. Elements of homology theory.....................................................................................8
   1. Products.................................................................................................................8
   2. Orientation of manifolds........................................................................................10
I. Topology of morphisms..............................................................................................12
   1. Set-valued maps....................................................................................................12
   2. Vietoris maps.........................................................................................................14
   3. Category of morphisms..........................................................................................18
   4. Operations in the category of morphisms..............................................................21
   5. Homotopy and extension properties of morphisms................................................23
   6. Essentiality of morphisms.......................................................................................28
   7. Concluding remarks................................................................................................32
II. The topological degree theory of morphisms............................................................33
   1. Cohomological properties of morphisms.................................................................34
   2. The fundamental cohomology class........................................................................36
   3. The topological degree of morphisms.....................................................................38
   4. The degree of morphisms of spheres and open subsets of Euclidean space..........43
   5. Borsuk type theorems..............................................................................................48
   6. Applications.............................................................................................................56
III. The class of approximation-admissible morphisms......................................................59
   1. Filtrations.................................................................................................................60
   2. Approximation-admissible morphisms and maps......................................................63
   3. Approximation of A-maps.........................................................................................68
IV. Approximation degree theory for A-morphisms...........................................................73
   1. The degree of A-morphisms.....................................................................................73
   2. Properties of the degree of A-morphisms................................................................75
   3. Further properties of the degree. Applications.......................................................78
V. Other classes of set-valued maps..............................................................................83
   1. Single-valued approximations..................................................................................83
   2. Linear filtrations. AP-maps of Petryshyn...................................................................91
   References..................................................................................................................97

Słowa kluczowe

set-valued mappings degree theory solvability of equations involving nonlinear operators fixed points of set-valued maps

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 336

Liczba stron

101

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCXXXVI

Daty

wydano

1994

otrzymano

1991-11-26

poprawiono

1993-07-14

Twórcy

autor

Wojciech Kryszewski

wkrysz@mat.uni.torun.pl

Instytut Matematyki, Uniwersytet Mikołaja Kopernika, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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1991 Mathematics Subject Classification: 54C60, 47H04, 55M25, 47H11, 47H10, 47H17, 54H25, 55M20.

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Topological and approximation methods of degree theory of set-valued maps

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