邻域系算子范畴及相关性质

The Category of Neighborhood System Operator and Its Relative Properties

对拓扑空间中的邻域系性质进行了进一步研究.提出了邻域系算子和邻域连续映射的概念,定义了邻域系算子范畴,讨论了该范畴上的余积和乘积,并证明了邻域系算子范畴与拓扑范畴是同构的2个范畴.

To make further study of the properties of neighborhood system in the topology,the definitions of neighborhood system operator and neighborhood continuous mapping are introduced.Then the definition of the category of neighborhood system operator is given and its product and coproduct are discussed.In the end of paper,it is proved that the category of neighborhood system operator is isomorphic to topological category.