Reconstructing Topological Graphs and Continua

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Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf;
(2015)
  • Subject: Mathematics - General Topology | Mathematics - Combinatorics | Primary 05C60, 54E45, Secondary 54B05, 54D05, 54D35, 54F15
    arxiv: Mathematics::General Topology
The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, 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 ... View more
  • References (20)
    20 references, page 1 of 2

    [1] J. M. Aarts and T. Nishiura, Dimension and Extensions, North-Holland Mathematical Library, Vol. 48, North-Holland, Amsterdam, 1993.

    [2] J. A. Bondy, A Graph Reconstructor's Manual, Surveys in combinatorics 166 (1991), 221-252.

    [3] R. E. Chandler, Hausdorff Compactifications, Lecture Notes in Pure and Applied Math, Vol. 23, Marcel Dekker, New York, 1976.

    [4] R. Diestel, Graph Theory, GTM 173, Springer Verlag, 3rd ed., 2005.

    [5] A. Dow and K. P. Hart, Cut Points in Cˇ ech-Stone Remainders, Proc. Amer. Math. Soc. 123(3) (1995), 909-917.

    [6] R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.

    [7] P. Gartside, M. F. Pitz and R. Suabedissen, Reconstructing Compact Metrizable Spaces, forthcoming.

    [8] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York, 1976.

    [9] W. Lewis, The pseudo-arc, Bol. Soc. Mat. Mexicana 3(5) (1999), 25-77.

    [10] K. D. Magill Jr, Countable compactifications, Can. J. Math. 18 (1966), 616-620.

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