关键词: 拓扑系统, Heyting系统, H-连续映射, H-空间化, 范畴

Abstract: Steven Vickers has proposed the topological system in his work "Topology via Logic" by synthesizing the methods of topology and the theory of logics,which also is applied to study of computers theory.Firstly,with the help of the idea of topological systems and the properties enjoyed by Frame structure and Heyting algebras,the new algebras system-Heyting system is put forward that takes the Heyting algebras as its principal body;Secondly, the suitable method of H-continuous mapping connecting Heyting systems is established;Thirdly,the representation of H-spatialization of a Heyting system is given,and related properties are investigated.The research methods of Heyting algebras and the research contents of topological system are enriched with the work of this paper.

Key words: topological system, heyting system, H-continuous mapping, H-spatialization, category