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Reconstructing topological graphs and continua
The {\it deck\/} of a topological space $X$ is the set ${\mathcal D}(X) =\{[X \setminus \{x\}] : x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is \emph {topologically reconstructible} if whenever ${\mathcal D}(X) ={\mathcal D