关于Locale范畴反射子范畴的注解

Notes on the Reflection Subcategory of the Category of Locales

利用Locale中的完全正则元和零维元构造性地给出了任意Locale的完全正则反射以及零维反射的描述,并且对于满足‘(?)’关系插入性的Locale,特别地,对正规Locale,证明了全体正则元构成的Locale是其正则反射.进而,利用平稳(flat)子Locale的扩张引理给出了Locale的紧完全正则反射,紧零维反射以及紧正则反射的构造性描述.

This paper applies completely regular elements and zero-dimensiomal elements, gives constructive descriptions of the completely regular reflection and the zero-dimensional reflection of Locales in much simple form. For a Locale A, which satisfies the subdivisibility property, especially a normal Locale, the authors show that the Locale R（A） of regular elements is the regular reflection of A. Furthermore, the compact regular reflection, the completely regular reflection and the compact zero-dimensional reflection of Locales by the extension lemma of flat suLocale are abtained.