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

Seria
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
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
  • Instytut Matematyki, Uniwersytet Mikołaja Kopernika, Chopina 12/18, 87-100 Toruń, Poland
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EN
Uwagi
1991 Mathematics Subject Classification: 54C60, 47H04, 55M25, 47H11, 47H10, 47H17, 54H25, 55M20.
Identyfikator YADDA
bwmeta1.element.zamlynska-32373e1d-eeec-49b0-80a5-033386ac06eb
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0012-3862
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DML-PL
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