点闭集值映射空间的分离性基础数学专业论文.docxVIP

ABSTRACT Topology properties of continuous multifunction spaces Ck ?X ,Y ?  with compact-open topology were widely discussed in many documents in 70-80s of the last century, and topologicians took great attention in pulling different topologies in multifunction spaces on the basis of different demands, such as topology of point-wise convergence, compact-open topology and topology of uniform convergence etc. Compact-open topology was the most important of all, and there were a lot of research results about it. In the recent years, multifunctions have much important application in many domains, for example in mathematical economics, measure theory and integral theory, and the discussions about topology properties of continuous multifunction spaces are increasing gradually. Separabilities are important properties of topological spaces, and the theories about the separabilities of single-valued continuous function spaces have already been relatively complete. Continuous multifunction spaces are more complicated than single-valued continuous function spaces, and the extension of point-closed continuous multifunction spaces is wider than that of point-compact continuous multifunction spaces, so obtaining the separabilities of the point-closed continuous multifunction spaces under ???open topology is the most general. In this paper, we discuss the separabilities of the point-closed continuous multifunction spaces C?X ,Y ??with ???open topology and obtain the internal relations between the separabilities of the point-closed continuous multifunction spaces and the separabilities of the image spaces by contrasting to point-compact continuous multifunction spaces and the hyperspace, therefor generalizing the separabilities of single-valued continuous function spaces , the separabilities of the point-compact continuous multifunction spaces under compact-open topology and the separabilities of the hyperspace to those of the point-closed continuous multifunc