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Convenient Closure Operators on \(\mathbb Z^2\)

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Book cover Combinatorial Image Analysis (IWCIA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5852))

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Abstract

We discuss closure operators on \(\mathbb Z^2\) with respect to which some cycles in a certain natural graph with the vertex set \(\mathbb Z^2\) are Jordan curves. We deal with several Alexandroff T 0-pretopologies and topologies and also one closure operator that is not a pretopology.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Brno University of Technology, 616 69, Brno, Czech Republic

    Josef Šlapal

Authors
  1. Josef Šlapal
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Editors and Affiliations

  1. Department of Automatic Control, Centro de Investigación y de Estudios Avanzados (CINVESTAV- IPN), Av. I.P.N. 2508, Col. San Pedro Zacatenco, 07000 D.F., Mexico

    Petra Wiederhold

  2. Department of Computer Science, State University of New York at Fredonia, NY 14063, Fredonia,, USA

    Reneta P. Barneva

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© 2009 Springer-Verlag Berlin Heidelberg

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Šlapal, J. (2009). Convenient Closure Operators on \(\mathbb Z^2\) . In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_33

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  • DOI: https://doi.org/10.1007/978-3-642-10210-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10208-0

  • Online ISBN: 978-3-642-10210-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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