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集值映射的连续选择 被引量:1

Coutinuous Selections for Set-valued Mappings
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摘要 本文推广了[1]中的结果,证明了如下定理,任何从仿紧拓扑空间到实轴的集值映射若具有凸闭像且几乎下半连续,则存在连续选择. Abstract In this paper,it is proved that any almost lower semicontinuous set-valued mappings with convex and closed images from a paracompact topological space to the real number axis always admits a continuous selection, which generalizes the result given in[1].
作者 王林
出处 《工程数学学报》 CSCD 1994年第1期89-93,共5页 Chinese Journal of Engineering Mathematics
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同被引文献4

  • 1DEUTSCH F, KENDEFOV. Continuous Selections and Approximate Selections for Set-Valued Mappings and Applications to Metric Projections[J]. SIAM J Math Anal, 1983(4) :185-194.
  • 2BARBU V, PRECPUANU T. The Convexity and Optimization in Banach Spaces[ M]. Romania, Buscuresti: Aca, Rep Soc,1978.
  • 3SINGER I. The Theory of Best Approximation and Functional Analysis[ M]. New York: Spinger Verlag, 1970.
  • 4MICKAEL E. Continuous Selections I[J]. Ann Of Math, 1956, 63:361-381.

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