247 decomposition of $D\times X$.

   247 decomposition of $D\times X$.

   248 The proof that these two maps are inverse to each other is the same as in

   248 The proof that these two maps are inverse to each other is the same as in

   249 Theorem \ref{product_thm}.

   249 Theorem \ref{product_thm}.

   250 \end{proof}

   250 \end{proof}

   251 

   251 

   252 

   253 

   253 \medskip

   254 \medskip

   254 

   255 

   255 The next theorem shows how to reconstruct a mapping space from local data.

   256 The next theorem shows how to reconstruct a mapping space from local data.

   256 Let $T$ be a topological space, let $M$ be an $n$-manifold, 

   257 Let $T$ be a topological space, let $M$ be an $n$-manifold,