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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 |
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252 This establishes Property \ref{property:gluing}. |
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, |