Injective hulls of $T\sb 0$ topological fibre spaces

We investigate the existence of injective hulls (with respect to the class of embeddings) in the categories Top_o/B$ of T_o topological fibre spaces over B. We prove that, if f:A----> B has a restriction to the image injective in Top_o/f(A), (A,f) has an injective hull in Top_o/B$ if and only if f(A') is locally closed in B, where A' denotes the union of non-indiscrete fibres of f.