三类特殊闭包空间的范畴性质

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

三类特殊闭包空间的范畴性质

尉文静, 李生刚*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2009-11-13 出版日期:2010-10-16 发布日期:2010-10-19
通讯作者: 李生刚（1959-），男，教授，博士生导师，研究方向为格上拓扑学与拟阵.
作者简介:尉文静（1986-），女，硕士研究生，研究方向为格上拓扑学.Email: yuwenjingdwj2006@163.com
基金资助:
国家自然科学基金资助项目（10871121）

Categorical properties of three kinds of special closure spaces

YU Wen-jing, LI Sheng-gang*

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

摘要/Abstract

摘要：

研究推理闭包空间范畴RCS、无底闭包空间范畴NCS以及代数闭包空间范畴ACS的性质。证明了RCS和NCS有乘积和余等值子但没有余积和等值子，ACS是一个topological construct,RCS是NCS的余反射满子范畴,并且ACS是CS (闭包空间范畴)的余反射满子范畴。

关键词: 闭包空间;推理闭包空间;无底闭包空间;代数闭包空间;topological construct;乘积;余积;余反射

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

尉文静, 李生刚*. 三类特殊闭包空间的范畴性质[J]. J4, 2010, 45(10): 73-77.

YU Wen-jing, LI Sheng-gang*. Categorical properties of three kinds of special closure spaces[J]. J4, 2010, 45(10): 73-77.

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