Some Results on Fibrewise Topological Spaces

In this paper we define and study new concepts of functions on fibrewise topological spaces over B namely, tibrewise weakly (resp., closure, strongly) continuous functions which are analogous of weakly (resp., closure, strongly) continuous functions and the main result is : Let p : X~ Y be a fibrewise closure (resp., weakly, closure, strongly, strongly) continuous function, where Y is fibrewise topological space over B and X is a fibrewise set which has the induced fibrewise topology. If for each fibrewise topological space Z, a fibrewise function jf : z~x is weakly (resp., continuous, closure, closure, weakly), then the composition q Ojf : Z~ Y is weakly (resp., weakly, closure, strongly, continuous). Also, we define and study the concepts fibrewise ro-closed (resp., ro-coclosed, (1)-biclosed, oo-open, oo-coopen, ro-biopen) topological spaces over B which is similar of definition of fibrewise closed (resp., open) topological spaces over B; also we state and prove several propositions concerning with these concepts.