关键词: 拓扑, 闭包算子, 连续映射, 积, 余积, 范畴同构

Abstract: Using the closure operation，closure operator space and the order between two closure operators on the given set are defined.It is proved that all closure operators on the given set constitute a complete lattice.At the same time，continuous mapping between two closure operator spaces is defined，thus closure operator space category which is proved to be an isomorphism category of topology space category is constructed.Simultaneously，It is proved that the product and coproduct space of some closure operator spaces exists.

Key words: topology, closure operation, continuous mapping, product, coproduct, category isomorphism