호남수학학술지 (Honam Mathematical Journal)

  • 제20권1호
  • /
  • Pages.135-145
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  • 1998
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

MICHAEL'S SELECTION THEORIES AND THEIR APPLICATIONS

  • CHO, MYUNG HYUN (Dept. of Mathematics, Wonkwang University)
  • 투고 : 1997.12.23
  • 발행 : 1998.07.30
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초록

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

키워드

과제정보

연구 과제 주관 기관 : NON DIRECTED RESEARCH FUND

참고문헌

  1. Studia Math. v.40 Extensions and selections of maps with decomposable values Bressan, A.;Colombo, G.
  2. Trudy. Moskov. Mat. Obshch. v.22 Multivalued maps and Borel sets. I Choban, M.M.
  3. Trans. Moscow Math. Soc. v.22 Choban, M.M.
  4. Trudy. Moskov. Mat. Obshch. v.23 Multivalued maps and Borel sets. II Choban, M.M.
  5. Trans. Moscow Math. Soc. v.23 Choban, M.M.
  6. General Topology Engelking, R.
  7. Inventiones Math. v.6 Topological well-ordering and continuous selections Engelking, R.;Heath, R.W.;Michael, E.
  8. Comment. Math. Univ. Carolinae v.35 no.3 Continuous selections, $G_{\delta}$-subsets of Banach spaces and usco mappings Gutev, V.G.
  9. Houston J. Math. v.21 no.3 Continuous selections on certain spaces Hattori, Y.;Nogura, T.
  10. Houston J. Math. v.12 no.2 Sections and selections McAuley, L.F.;Addis, D.F.
  11. Ann. of Math. v.63 Continuous selections I Michael, E.
  12. Ann. of Math. v.64 Continuous selections II Michael, E.
  13. Duke Math. J. v.26 no.4 A theorem on semi-continuous set-valued functions Michael, E.
  14. Fund. Math. v.111 Continuous selections and countable sets Michael, E.
  15. Open Problems in Topology Michael, E.;van Mill, J.(ed.);Reed, J.M.(ed.)
  16. Fund. Math. v.140 Some refinements of a selection theorem with 0-dimensional domain Michael, E.
  17. J. Math. Anal. Appl. v.19 Set-valued generalizations of Baire's category theorem Urbaniec, P.