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

Document Type: Research Paper

Author

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

Abstract

Employing the notions of the strong $L$-topology introduced by Zhang
and the $L$-frame introduced by Yao  and the concept of $L$-enriched
topological system defined in the present paper, we construct
adjunctions 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 these
concepts are essentially based on the theory of $L$-enriched
categories, thus we obtain a unified enriched-categorical version of
the classical adjunctions among the categories {\bf Top} of
topological spaces, {\bf Loc} of locales and {\bf TopSys} of
topological systems, as well as a unified enriched-categorical
approach to treating these concepts.

Keywords


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