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Reconstructing topological graphs and continua

Volume 148 / 2017

Paul Gartside, Max F. Pitz, Rolf Suabedissen Colloquium Mathematicum 148 (2017), 107-122 MSC: Primary 05C60, 54E45; Secondary 54B05, 54D05, 54D35, 54F15. DOI: 10.4064/cm7011-10-2016 Published online: 24 February 2017


The 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 topologically reconstructible if whenever ${\mathcal D}(X) ={\mathcal D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more generally, that all compact graph-like spaces are reconstructible.


  • Paul GartsideThe Dietrich School
    of Arts and Sciences
    301 Thackeray Hall
    Pittsburgh, PA 15260, U.S.A.
  • Max F. PitzDepartment of Mathematics
    University of Hamburg
    Bundesstraße 55 (Geomatikum)
    20146 Hamburg, Germany
  • Rolf SuabedissenMathematical Institute
    University of Oxford
    Oxford OX2 6GG, United Kingdom

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