Digital surfaces and boundaries in Khalimsky spaces
2007 (English)In: Journal of Mathematical Imaging and Vision, ISSN 0924-9907, E-ISSN 1573-7683, Vol. 28, no 2, 169-177 p.Article in journal (Refereed) Published
Let X be a smallest-neighborhood space, sometimes called an Alexandrov space. We demonstrate that the graph of a Khalimsky-continuous mapping X->Z is a surface having a Jordan--Brouwer type separation property. We study infima and suprema of families of such continuous mappings, a study that naturally leads to the introduction of an extended Khalimsky line. Moreover, we show that the boundary of a connected subset, U, of the Khalimsky plane is connected precisely when the complement of U is connected.
Place, publisher, year, edition, pages
2007. Vol. 28, no 2, 169-177 p.
IdentifiersURN: urn:nbn:se:uu:diva-96676DOI: 10.1007/s10851-007-0006-9ISI: 000248978600006OAI: oai:DiVA.org:uu-96676DiVA: diva2:171327