Alexandroff L-co-topological spaces

  • Authors:

  • Piwei Chen;Dexue Zhang

  • Affiliations:

  • Department of Mathematics, Sichuan University, Wangjianglu 29, Chengdu 610064, China;Department of Mathematics, Sichuan University, Wangjianglu 29, Chengdu 610064, China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-topological spaces is the coreflective hull of the subcategory of finite strong L-co-topological spaces in the category of strong L-co-topological spaces. So, the results illustrate an essential difference between topology and co-topology in the many valued setting.