"quasi-discrete pretopology, quotient pretopology, connectedness graph, digital plane, Jordan curve"@en . "A Jordan curve theorem with respect to a pretopology on Z^2"@en . . "11"^^ . "A Jordan curve theorem with respect to a pretopology on Z^2" . "8" . "1"^^ . . . . . "90" . . "RIV/00216305:26210/13:PU101371!RIV14-MSM-26210___" . "P(ED1.1.00/02.0070)" . . . . . . "RIV/00216305:26210/13:PU101371" . "\u0160lapal, Josef" . . "We study a pretopology on $\\mathbb Z^2$ 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."@cs . "A Jordan curve theorem with respect to a pretopology on Z^2" . "26210" . "We study a pretopology on $\\mathbb Z^2$ 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."@en . . . . . . "We study a pretopology on $\\mathbb Z^2$ 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." . . "0020-7160" . "International Journal of Computer Mathematics" . "58666" . "A Jordan curve theorem with respect to a pretopology on Z^2"@cs . "[127D26BA8B03]" . "A Jordan curve theorem with respect to a pretopology on Z^2"@cs . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "1"^^ . "A Jordan curve theorem with respect to a pretopology on Z^2"@en .