J4 ›› 2010, Vol. 45 ›› Issue (10): 73-77.

• Articles • Previous Articles     Next Articles

Categorical properties of three kinds of special closure spaces

YU Wen-jing, LI Sheng-gang*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2009-11-13 Online:2010-10-16 Published:2010-10-19

Abstract:

Properties of the category RCS of reasoning closure spaces, the category NCS of bottomless closure spaces and the category ACS of algebraic closure spaces are studied. It is proved that the categories RCS and NCS have products and coequalizers, but have no coproduct and equalizer, ACS is a topological construct, RCS is a coreflective full subcategory of NCS, and ACS is a coreflective full subcategory of CS.

Key words:  Closure space; reasoning closure space; bottomless closure space; algebraic closure space; topological construct; product; coproduct; coreflection

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