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

100%

Ma T.-W.

Instytut Matematyczny Polskiej Akademii Nauk

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

Non-singular set-valued compact fields in locally convex spaces

37%

Ma T.-W.

Fundamenta Mathematicae

1972

tom 75

nr 3

249-259

Ograniczanie wyników

1 Fundamenta Mathematicae

2 Ma T.-W.

2 1972

Wyniki wyszukiwania

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

Non-singular set-valued compact fields in locally convex spaces