Research On P Open Sets And Their Related Topological Properties In Topological Spaces

In general topology, we studied the open sets and the topological properties. In 1956, Njastad defined semi-open set????-openset and preopen set on the basis of the definition of open set. On this basis, many scholars study the topological properties of semi-set, including semi-internal, semi-closures and semi-separation, semi-connectivity of topological space and so on. In this paper, we define p-continuous mapping, p-irreducible mapping and p-homeomorphism mapping and introduce the p-compact space and p-Lindel(?)f spaces. Moreover, we study their properties. This paper is parted into three chapters,In Chapter 1, we introduce the background of p-open set and give necessary symbols and preliminanies which are used in this paper.In Chapter 2, we discuss the properties of p-open set, and give the definition of p-continuous mapping, p-irreducible mapping and p-homeomorphism mapping.In Chapter 3, we introduced the p-separation axioms, and dis-cusses their properties, and define p-compact space and p-Lindel(?)f space. We study the topological properties of p-compact space and p-Lindel(?)f space.