数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1366-1374.doi: 10.1016/S0252-9602(09)60109-0

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GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

 李庆国, 伍秀华   

  1. College of Mathematics and Econometrics, Hunan University, Changsha 410082, |China
  • 收稿日期:2007-01-28 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:

    Sponsored by the  NSFC (10471035, 10771056)

GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

 LI Qiang-Guo, WU Xiu-Hua   

  1. College of Mathematics and Econometrics, Hunan University, Changsha 410082, |China
  • Received:2007-01-28 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    Sponsored by the  NSFC (10471035, 10771056)

摘要:

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also
semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

关键词: semicontinuous lattices, strongly semicontinuous lattices, semicontinuous mapping, hereditary,  function space,  Cartesian closed category

Abstract:

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also
semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

Key words: semicontinuous lattices, strongly semicontinuous lattices, semicontinuous mapping, hereditary,  function space,  Cartesian closed category

中图分类号: 

  • 06A15