In this paper we define and study new concepts of functions on fibrewise topological spaces over B namely, fibrewise weakly (resp., closure, strongly) continuoac; funttions which are analogous of weakly
(resp., closure, strongly) continuous functions and the main result is : Let <p : XY 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 \jl : z x is weakly (resp., continuous, closure, closure, weakly), then the composition q>O'fl : z Y is weakly (resp.•
weakly, closure, strongly, continuous). Also, we define and study the concepts fibrewise ro-closed (resp., ro·coclosed, (i}·biclosed, ID·open, co-coopen, ro·biopen) topological spaces over B which is similar of definition of fibrewise c1osed (resp., open) topological spaces over B; also we state and prove several propositions concerning with these concepts.
