数学季刊 ›› 1992, Vol. 7 ›› Issue (4): 51-55.

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Some Properties of Two Kinds of Multifunctions

  


  1. Dept. Math. Tianjin University Tianjing 300072

  • 收稿日期:1990-12-05 出版日期:1992-12-30 发布日期:2025-06-20
  • 基金资助:
    This paper was reported at the 5th National Functional Analysis Conference held at Nanjing in Nov.,1990.

Some Properties of Two Kinds of Multifunctions


  1. Dept. Math. Tianjin University Tianjing 300072
  • Received:1990-12-05 Online:1992-12-30 Published:2025-06-20
  • Supported by:
    This paper was reported at the 5th National Functional Analysis Conference held at Nanjing in Nov.,1990.

摘要: Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.

关键词:  , process, fan, upper semicontinuous, lower semicontipuous, subclosed graph, multi-homomor- phism

Abstract: Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.

Key words:  , process, fan, upper semicontinuous, lower semicontipuous, subclosed graph, multi-homomor- phism