JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (11): 90-96.doi: 10.6040/j.issn.1671-9352.0.2018.532

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Open remote neighborhoods of topological systems and their applications

FENG Dan-dan, WU Hong-bo*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2019-11-06

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Abstract: 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.

Key words: topological system, open remote neighborhood, open remote neighborhood system, continuous mapping, T0 topological system, T1 topological system

CLC Number: 

  • O141.1
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