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Another Jordan Curve Theorem in the topological space (Z^2,w).
As an alternative to the Khalimsky topology, the topology w on the digital plane Z^2 was introduced by the author of this note who also proved a Jordan curve theorem for it. It the present paper, another Jordan
Pure mathematics
- 2014 •
- D
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D - Stať ve sborníku
Digital Jordan curves with respect to a closure operator
We introduce 2D digital Jordan curves as the curves satisfying a digital Jordan curve theorem. The theorem builds on the connectedness in the digital plane Z2 provided by a closure operat...
Applied mathematics
- 2020 •
- D •
- Link
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D - Stať ve sborníku
Výsledek na webu
A digital analogue of the Jordan curve theorem
We study certain closure operations on the digital plane and prove a digital analogy of the Jordan curve theorem for them.
BA - Obecná matematika
- 2004 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A Jordan Curve Theorem with Respect to Certain Closure Operations on the Digital Plane
We introduce and study closure operations on ZxZ which generalize the Khalimsky topology.By proving a digital analogy of the Jordan curve theorem for these closure operations, we show that they are suitable for solving prob...
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Jordan curve theorems with respect to certain pretopologies on Z^2
We study Jordan curves with respect to certain pretopologies on Z^2...
BA - Obecná matematika
- 2009 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A Jordan curve theorem in the digital plane
We study a certain Alexandroff topology on $mathbb Z^2$ and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan curve theorem for this topology we show that it provides a large ...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
An alternative digital topology
We define a new topology on the digital plane and formulate a digital Jordan curve theorem with respect to it.
BA - Obecná matematika
- 2003 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A Jordan curve theorem with respect to a pretopology on Z^2
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 showin...
BA - Obecná matematika
- 2013 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Digital Jordan curves
A new topology is defined on the digital plane and then studied. In particular, an analogy of the Jordan curve theorem is proved for this topology....
BA - Obecná matematika
- 2006 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A digital pretopology and one of its quotients
We introduce a certain pretopology on the digital plane $mathbb Z^2$ and present a digital analogue of the Jordan curve theorem for for it. We then discuss a topology on $mathbb Z^2$ which is shown to be a quotient pretopol...
BA - Obecná matematika
- 2012 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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