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

Tsoy-Wo Ma

GDML_Books, (1972), p.

Résumé

CONTENTSIntroduction................................................................................................................................................. 5I. General properties of set-valued compact fields............................................................................. 61. Upper semicontinuous maps............................................................................................................. 62. Generalization of Dugundji's extension theorem............................................................................ 73. Set-valued compact fields................................................................................................................... 94. Reduction to finite dimensional vector spaces............................................................................... 105. Reduction to single-valued compact fields...................................................................................... 12II. Topological degrees of set-valued compact fields in locally convex spaces............................. 166. Basic known facts about Brouwer's degrees................................................................................... 167. Definition of topological degree and its homotopy invariance...................................................... 178. Sum theorem.......................................................................................................................................... 209. The case of odd degrees..................................................................................................................... 2210. The case of non-vanishing degrees................................................................................................ 2511. Reduction formula............................................................................................................................... 2812. Translation invariance and component dependence.................................................................. 2913. Product of domains............................................................................................................................. 3014. Generalized Hopf theorem for metrizable locally convex spaces.............................................. 3115. Product theorem for composite maps............................................................................................ 33III. Extension of some classical results to set-valued maps............................................................. 3816. Fixed point theorems and fixed point indices................................................................................ 3817. Extension of Borsuk's sweeping theorem...................................................................................... 3918. Extension of Borsuk-Ulam's theorem............................................................................................. 4019. Extension of Brouwer's invariance of domains............................................................................. 40References.................................................................................................................................................. 43

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Zbl 0211.25903

EUDML-ID : urn:eudml:doc:268504