Reconstructing Compact Metrizable Spaces

@article{Gartside2015ReconstructingCM,
  title={Reconstructing Compact Metrizable Spaces},
  author={Paul Gartside and Max Pitz and Rolf Suabedissen},
  journal={arXiv: General Topology},
  year={2015}
}
The deck, $\mathcal{D}(X)$, of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}]\colon x \in X\}$, 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) continuum is reconstructible, whereas the Cantor set is non-reconstructible. The main result of this paper characterises the non-reconstructible compact metrizable… Expand
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RECONSTRUCTION OF FINITE TOPOLOGICAL SPACES WITH MORE THAN ONE ISOLATED POINT
The deck of a topological space X is the set D(X) = {[X − {x}] : x ∈ X}, where [Z] denotes the homeomorphism class of Z. A space X is topologically reconstructible if whenever D(X) = D(Y ) then X isExpand

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