Reconstructing compact metrizable spaces
Reconstructing compact metrizable spaces
The deck, $\mathcal {D}(X)$, of a topological space $X$ is the set $\mathcal {D}(X) =\{[X \setminus \{x\}]:x \in X\}$, where $[Y]$ denotes the homeomorphism class of $Y$. A space $X$ is (topologically) reconstructible if whenever $\mathcal {D}(Z)=\mathcal D(X)$, then $Z$ is homeomorphic to $X$. It is known that every (metrizable) …