In the category of topological spaces, a fibre space (E, X, p) is a triple of a morphism (continuous map) p of E to X.
If j is a monomrphism of x to X where x is a final object, the fibre of x is a pull back of j and p.
If E is the product of X and F (its topology may not be the product topology) and p is the projection of E on X (need to be continuous), then call it a trivial fibre space over X with fibre F.
Now, my question is whether the fibre of x isomorphic (homeomorphic) to F.
I know it is true for E with the product topology, however,in 1.4 of Grothendieck's "A general theory of fibre spaces with structure sheaf", discussing more generally but without explanations.