 Consider the space formula_34 modulo the equivalence relation formula_35 is equivalent to formula_36 if and only if formula_30 and consider formula_38 to be a map formula_39 then we demand that formula_40.That is, in our re-construction of formula_22 we are replacing the fibre formula_5 by the topological group of homeomorphisms of the fibre, formula_43.If the structure group of the bundle is known to reduce, you could replace formula_43 with the reduced structure group.