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Section A

A Jordan curve theorem with respect to a pretopology on ℤ2

Pages 1618-1628 | Received 13 Apr 2012, Accepted 17 Oct 2012, Published online: 14 Feb 2013
 

Abstract

We study a pretopology on ℤ2 having the property that the Khalimsky topology is one of its quotient pretopologies. Using this fact, we prove an analogue of the Jordan curve theorem for this pretopology, thus showing that such a pretopology provides a large variety of digital Jordan curves. Some consequences of this result are discussed too.

2010 AMS Subject Classifications: :

Acknowledgements

This work was supported by the IT4Innovations Centre of Excellence project CZ.1.05/1.1.00/02.0070 and by the Brno University of Technology Grant Agency, project no. FSI-S-11-3.

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