A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Abstract

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image