Example 2

Example 1 is generalized as follows. Let B and F be topological spaces and let G be a topological group operating continuously on the left in F. By passing to the quotients, the mapping of $B\times F$ into $(B\times G)\times F$ given by $(b, f)\mapsto ((b, e), f)$ and the mapping of $(B\times G)\times F$ into $B\times F$ given by $((b, g), f)\mapsto (b, gf)$ define reciprocal B-isomorphisms $B\times F\rightarrow (B\times G)\times^GF$ and $(B\times G)\times^GF\rightarrow B\times F$.