拓扑系统中开远域及其应用

在拓扑系统中提出了点的开远域的概念并对其性质和应用进行了研究。首先,在拓扑系统中提出了点的开远域的概念,讨论了它的基本性质,并利用开远域系给出了确定拓扑系统的方法;其次,通过开远域系定义了拓扑系统之间的映射在给定点连续的定义,并由此给出了拓扑系统之间连续映射的等价刻画;最后,利用点的开远域系给出T0拓扑系统和T1拓扑系统的等价刻画。

Open remote neighborhoods of topological systems and their applications

The concept of open remote neighborhood is proposed in topological system, and its properties with applications are studied. At first, the concept of open remote neighborhood is proposed in topological system, and its basic properties are discussed. Furthermore, a method of determining topological system is given by open remote neighborhood systems. The definition of continuous of mapping at a fixed point between topological systems is defined by open remote neighborhood systems, by which the equivalent form of continuous mapping between topological systems is given. At last, the equivalent forms of some separations of topological systems are given by using the open remote neighborhood systems.