Journal title
Colloquium Mathematicum
DOI
10.4064/cm7011-10-2016
Issue
1
Volume
148
Last updated
2022-03-06T20:27:22.81+00:00
Page
107-122
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.
Symplectic ID
569838
Submitted to ORA
On
Publication type
Journal Article
Publication date
24 February 2017