대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제16권2호
  • /
  • Pages.277-285
  • /
  • 2001
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

A PROOF OF A CONVEX-VALUED SELECTION THEOREM WITH THE CODOMAIN OF A FRECHET SPACE

  • Cho, Myung-Hyun (Department of Mathematics, Wonkwang University) ;
  • Kim, Jun-Hui (Department of Mathematics Sciences, Faculty of Science, Ehime University)
  • 발행 : 2001.04.01
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초록

The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

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참고문헌

  1. Topoogies on closed and closed convex sets G. Beer
  2. Bull. of Korean Math. Soc. v.36 Continuous selections under weaker separation axioms and reflexive Banach spaces Myung Hyun Cho
  3. General Topology R. Engelking
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  5. Proc. London Math. Soc. v.80 Selections for Vietories-like hyperspace topologies V. G. Gutev;T. Nogura
  6. Trans. Amer. Math. Soc. v.71 Topologies on spaces of subsets E. Michael
  7. Canad. J. Math. v.11 Convex structures and continuous selections
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  12. Modern general topology(the second revised ed.) J. Nagata
  13. Serdica v.6 Selection and factorization theorems for set-valude mappings S. I. Nedev
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  15. Continuous selections of multivalued mappings