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Connectivity Spaces

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Abstract

Connectedness is a fundamental property of objects and systems. It is usually viewed as inherently topological, and hence treated as derived property of sets in (generalized) topological spaces. There have been several independent attempts, however, to axiomatize connectedness either directly or in the context of axiom systems describing separation. In this review-like contribution we attempt to link these theories together. We find that despite differences in formalism and language they are largely equivalent. Taken together the available literature provides a coherent mathematical framework that is not only interesting in its own right but may also be of use in several areas of computer science from image analysis to combinatorial optimization.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany

    Bärbel M. R. Stadler & Peter F. Stadler

  2. Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinformatics, University of Leipzig, Härtelstrasse 16-18, 04107, Leipzig, Germany

    Peter F. Stadler

  3. RNomics Group, Fraunhofer Institut für Zelltherapie und Immunologie, Deutscher Platz 5e, 04103, Leipzig, Germany

    Peter F. Stadler

  4. Department of Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090, Vienna, Austria

    Peter F. Stadler

  5. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA

    Peter F. Stadler

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  1. Bärbel M. R. Stadler
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  2. Peter F. Stadler
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Correspondence to Peter F. Stadler.

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This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) Project STA850/11-1 within the EUROCORES Programme EuroGIGA (project GReGAS) of the European Science Foundation and Project STA 850/14-1 within SPP 1590 “Probabilistic Structures in Evolution”.

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Stadler, B.M.R., Stadler, P.F. Connectivity Spaces. Math.Comput.Sci. 9, 409–436 (2015). https://doi.org/10.1007/s11786-015-0241-1

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