Convenient Closure Operators on $\mathbb Z^2$

Authors:
Josef Šlapal
Affiliations:
Department of Mathematics, Brno University of Technology, Brno, Czech Republic 616 69
Venue:
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Year:
2009

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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.