拓扑系统范畴与子拓扑系统

Category of topological systems and sub-topological systems

拓扑系统是目前最广泛的拓扑学研究对象，它以点集拓扑空间、Ｌｏｃａｌｅ的空间化、模糊拓扑空间与拓扑分子格为特例，它可用来研究计算机程序语言的指称语义的Ｄｏｍａｉｎ理论．拓扑系统与它们的连续映射构成一个范畴，本文讨论这一范畴的基本理论，并引入子拓扑系统概念，得到了拓扑系统Ｄ可嵌入拓扑系统Ｅ中当且仅当Ｄ同胚于Ｅ的某子拓扑系统．

The concept of topological system is a common generalizaton of tbhoe ofspatializatons of locales,topological spaces,fuzzy topological spaces and topological molecularlattices. It also models the domain cheory of denotational semantics in computerprogramming languanges. Topological systems and continuous functions forms a category.The author discuss this category and introcluce a concept of sub-topological systems, andprove that topological system D is embedable in topological system E if and only if D ishomeomorphic to some sub-topological system of E.