A Generalization Of Fibrewise Separation Condition In The Generalized Fibrewise Topological Category

The fibrewise separation condition holds important status in the TOP_b category(the objects are the fibrewise topological spaces over B,for two objects (X,p) and (Y, q),a morphism from X to Y is a continuous map such that p=q o Φ.).It has some interesting properties.Namely,in the TOPb category,a morphism preserves(inversely preserves)the fibrewise separation condition when it satisfies certain condition.Combined with the analysis of the existed properties,the conditions of the morphism which also preserves (inversely preserves)the fibrewise separation condition in the TOP_* category(the object are the fibrewise topological spaces over different bases,for two objects a morphism from X to Y is a pair Φ, λ of continuous maps such that λ o f = g o Φ) are given.Here is the outline of thesis:1,morphism (Φ, λ),fibrewise R₀,fibrewiseT_i(i = 0,1, 2),fibrewise(completely) regular, fibrewise(functionaHy)normal are preserved when Φ is open continuous fibrewise surjection and A is open continuous map.2,morphism( (Φ, λ)),fibrewise R₀ and fibrewise(completely)regular are inversely preserved when Φ is open continuous fibrewise surjection and λ is continuous mapping;fibrewise(functionally)normal is inversely preserves when Φ is closed continuous fibrewise injection and λ is continuous map.