Corollary 1

Let B be a paracompact topological space, let G be a topological group and let $(E, p)$ be a principal fibre $B\times \mathbf{I}$-space of group G. For $t\in \mathbf{I}$, let $(E_t, p_t)$ denote the principal fibre B-space $i^*_tE$, where $i_t: B\rightarrow B\times \{t\}$ is the mapping $b\mapsto (b, t)$. The principal fibre B-spaces $E_0$ and $E_t$ are isomorphic for every $t\in \mathbf{I}$.