publication . Preprint . Article . 2015

Reconstructing Topological Graphs and Continua

Paul Gartside; Max Pitz; Rolf Suabedissen;
Open Access English
  • Published: 24 Sep 2015
  • Country: United Kingdom
Abstract
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 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.
Subjects
arXiv: Mathematics::General Topology
free text keywords: Mathematics - General Topology, Mathematics - Combinatorics, Primary 05C60, 54E45, Secondary 54B05, 54D05, 54D35, 54F15, Discrete mathematics, Graph, Mathematics
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