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Topological degrees of set-valued compact fields in locally convex spaces

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Rozprawy Matematyczne tom/nr w serii: 92 wydano: 1972
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CONTENTS
Introduction................................................................................................................................................. 5
I. General properties of set-valued compact fields............................................................................. 6
1. Upper semicontinuous maps............................................................................................................. 6
2. Generalization of Dugundji's extension theorem............................................................................ 7
3. Set-valued compact fields................................................................................................................... 9
4. Reduction to finite dimensional vector spaces............................................................................... 10
5. Reduction to single-valued compact fields...................................................................................... 12
II. Topological degrees of set-valued compact fields in locally convex spaces............................. 16
6. Basic known facts about Brouwer's degrees................................................................................... 16
7. Definition of topological degree and its homotopy invariance...................................................... 17
8. Sum theorem.......................................................................................................................................... 20
9. The case of odd degrees..................................................................................................................... 22
10. The case of non-vanishing degrees................................................................................................ 25
11. Reduction formula............................................................................................................................... 28
12. Translation invariance and component dependence.................................................................. 29
13. Product of domains............................................................................................................................. 30
14. Generalized Hopf theorem for metrizable locally convex spaces.............................................. 31
15. Product theorem for composite maps............................................................................................ 33
III. Extension of some classical results to set-valued maps............................................................. 38
16. Fixed point theorems and fixed point indices................................................................................ 38
17. Extension of Borsuk's sweeping theorem...................................................................................... 39
18. Extension of Borsuk-Ulam's theorem............................................................................................. 40
19. Extension of Brouwer's invariance of domains............................................................................. 40
References.................................................................................................................................................. 43
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 92
Liczba stron
43
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom XCII
Daty
wydano
1972
Twórcy
autor
Bibliografia
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