Volume 37 • Number 2 • 2014   • 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