J4 ›› 2010, Vol. 45 ›› Issue (4): 74-76.

• Articles • Previous Articles     Next Articles

Products, sums, and quotients of M-closure spaces

ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu   

  1. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2009-01-17 Online:2010-04-10 Published:2010-05-19

Abstract:

The notions of M-closure space and continuous mapping between two M-closure spaces are defined. It is proved that the category M-CS of all M-closure spaces and continuous mappings between them is a topological construct, but not cartesian closed (where M is any nonempty index set). Based on this, the notions of product M-closure spaces, sum M-closure spaces, and quotient M-closure spaces are defined. Finally, it is pointed out  that M-closure systems and M-weak closure operators can determine each other.

Key words:  M-closure spaces; topological construct; product M-closure spaces; sum M-closure spaces; quotient M-closure spaces; cartesian closed category; M-weak closure operators

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