Corollary 1

Let B be a paracompact topological space and let $(E, p)$ be a locally trivial fibre space over $B\times \mathbf{I}$ (I, p. 71, Corollary 2). For $t\in \mathbf{I}$, let us denote by $(E_t, p_t)$ the locally trivial fibre space over B $i^*_tE$, where $i_t: B\rightarrow B\times \{t\}$ is the mapping $b\mapsto (b, t)$. The locally trivial fibre spaces over B $E_0$ and $E_t$ are isomorphic for every $t\in \mathbf{I}$.