Research On Semi-open And Semi-continuous Mapping In Topological Space

N. L. Levine defined semi-open set and semi-continuous mapping. Furthermore, N. L. levine studied their topological properties. Later, many scholars performed further study on them. This thesis investi-gates two problems of topological space. The first is to research the property of the semi-open set; the second is to study the properties of the semi-continuous mapping and the mappings which are defined on semi-open set. Particularly,In Chapter 1, we introduce the definition and the background of semi-open set, at the same time, we give the necessary symbols and preliminaries which are used in this paper.In Chapter 2, we give the definitions of semi-separation spaces, semi-compact spaces and semi-connected spaces. Furthermore, we study the properties of semi-separation spaces and semi-compact spaces and semi-connected spaces.In Chapter 3, we give the definitions of semi-continuous map-pings?semi-open mappings?semi-close mappings?strong semi-open mappings and strong semi-close mappings by using semi-open sets, and study their properties.