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| Volume 37 • Number 2 • 2014 |
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Jordan Curves in the Digital Plane
Josef Šlapal
Abstract.
We discuss certain interrelated pretopologies on the digital plane ℤ^2 including the Khalimsky topology and several other topologies on ℤ^2. We present a digital analogue of the Jordan curve theorem for each of the pretopologies to demonstrate that they can provide background structures on ℤ^2 convenient for the study of geometric and topological properties of two-dimensional digital images.
2010 Mathematics Subject Classification: Primary 52C99; Secondary 54B15, 68C05
Full text: PDF
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