$L$-enriched topological systems---a common framework of $L$-topology and $L$-frames

نویسندگان

1 School of Sciences, Chang'an University, Xi'an, China

doi
10.22111/ijfs.2014.1725
چکیده

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {\bf St$L$-Top} of strong$L$-topological spaces, {\bf S$L$-Loc} of strict $L$-locales and{\bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are essentially based on the theory of $L$-enrichedcategories, thus we obtain a unified enriched-categorical version ofthe classical adjunctions among the categories {\bf Top} oftopological spaces, {\bf Loc} of locales and {\bf TopSys} oftopological systems, as well as a unified enriched-categoricalapproach to treating these concepts.