The Product Space In The Generalized Fibrewise Topological Spaces Category

Content abstract:The fibrewise topological product space occupies very important position in the topological theory. Properties of the product space have a direct relationship with the generation of its space. Many properties of fibrewise topological space is productivity.In this paper, on the basis of the generalization of fibrewise topological product space.Mainly discussed the form of fibrewise topological product spaces with different base And what properties the fibrewise product topological space has. At the same time is also discussed in this paper, the different mapping condition, keep some properties of product space.The main contents of this paper:1、The define of the product space of generalized fibrewise topological spaces and some mapping of retention.2、When the fibrewise topological space(Xi,pi,Bi),i∈Γ are fibrewiseTi(i=0,1,2), fibrewise (function) regular, fibrewise completely regular.The product space have such properties.3、Fibrewise compact and fibrewise Ro of the product space of generalized topological.The main conclusions of this paper:Proposition3.2.1Fibrewise topological space(X1,p1,B1),(X2,p2,B2), if X1, X2is fibrewise open (closed).Then (X1×X2,p3,Bx×B2) is fibrewise open (closed).Proposition4.1.1(Xi,pi,Bi,i∈Γ be a family of fibrewise topological spaces, if (Xi, pi,Bi) are fibrewise Ti(i=0,1).Then the product space is fibrewise Ti(i＝0,1).Proposition4.2.3(Xi,pi,Bi),i∈Γbe a family of fibrewise topological spaces. if (Xi,pi,Bi) are fibrewise function T2. Then the product space fibrewise function.Proposition4.3.1(Xi,pi,Bi),i∈Γ be a family of fibrewise topological spaces. if (Xi,pi,Bi) are fibrewise regular.Then the product space is fibrewise regular.Proposition5.1.1Fibrewise topological space (X1,p1,B1),(X2,p2,B2), ifX1,X2 is fibrewise compact, then the product space (X1×X2,p3,B1×B2) is fibrewise compact.Proposition5.2.1Fibrewise topological space (X1,p1,B1),(X2,p2,B2), if X1, X2is the fibrewise Ro, then the product space (X1×X2,p3,B1×B2) is fibrewise R0.