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Reconstructing topological graphs and continua

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 gene...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.4064/cm7011-10-2016

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics) Publisher's website
Journal:
Colloquium Mathematicum Journal website
Volume:
148
Pages:
107-122
Publication date:
2017-02-24
Acceptance date:
2016-10-06
DOI:
EISSN:
1730-6302
ISSN:
0010-1354
Pubs id:
pubs:569838
URN:
uri:e8e2a445-5782-40f7-8988-1ede0d5c1fce
UUID:
uuid:e8e2a445-5782-40f7-8988-1ede0d5c1fce
Local pid:
pubs:569838

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