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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (5): 614-617.

• 论文 • 上一篇    下一篇

ON THE ISOMETRIC ISOMORPHISM OF PROBABILISTIC METRIC SPACES

刘明学   

  1. Department of Mathematics, Changsha University, Changsha 410003, P. R. China
  • 收稿日期:1999-12-15 修回日期:2001-11-20 出版日期:2002-05-18 发布日期:2002-05-18
  • 基金资助:
    the Foundation of Education Committee of Fujian Province(JA99156)

ON THE ISOMETRIC ISOMORPHISM OF PROBABILISTIC METRIC SPACES

LIU Ming-xue   

  1. Department of Mathematics, Changsha University, Changsha 410003, P. R. China
  • Received:1999-12-15 Revised:2001-11-20 Online:2002-05-18 Published:2002-05-18
  • Supported by:
    the Foundation of Education Committee of Fujian Province(JA99156)

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摘要： There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E,F) is isometrically isomorphic to another PM space (E',F'), and the second is that a PM space (E,F) is isometrically isomorphic to a generating space of quasi-metric family (E',dr,r∈(0,1)). This paper establishes the connection between the two kinds of isometric isomorphism.

Abstract: There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E,F) is isometrically isomorphic to another PM space (E',F'), and the second is that a PM space (E,F) is isometrically isomorphic to a generating space of quasi-metric family (E',dr,r∈(0,1)). This paper establishes the connection between the two kinds of isometric isomorphism.

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