拓扑系统范畴完备性与Tychonoff乘积定理

Completeness of the Category of Topological System and Tychonoff Product Theorem

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，用它可研究计算机程序设计语言指称语义的Domain理论．本文旨在建立拓扑系统范畴的乘积结构与等子结构，表明拓扑系统范畴是完备范畴．讨论拓扑系统的紧性，得到了拓扑系统关于紧性的Tychonoff乘积定理．

The topological system is the most widely studied object in topology at present.Topopogical space, spatialization Of locale, fuzzy topological space and topological molecular lattice are its special cases. on can study Domain theory on denotatioal semantics of computer progrmming lauguages by using the topological system. This paper establishes the structures of equalizer and product of the category of topological system, and shows that the category of topological system is complete. The paper also discusses the compactness of topological system,and obtains Tychonoff product theorem of topological system on compactness.