The Pointless Description Of Some Fibrewise Topological Properties

ABSTRACT:Fibrewise Topology is a branch of modern topology theory, which develops very quickly. Recently, many mathematicians have taken tremendous interest in this subject. Meanwhile, the theory about DCPO in Theoretical Computer Science has been also paid much attention to, to which the theory of Frames supplies a lot of important reasoning. In this paper, the pointless description of some fibrewise topological properties, such as open maps, close maps, fibrewise regular, maps and fibrewise normal maps, will be discussed. Accordingly, the application of the fibrewise viewpoint to the theory of Frames will be convenient. Under the pointless description, some properties of fibrewise regular and fibrewise normal will be also obtained.