A Jordan surface theorem for three-dimensional digital spaces
Discrete & Computational Geometry
A topological approach to digital topology
American Mathematical Monthly
Semi-metrics, closure spaces and digital topology
Selected papers of the workshop on Topology and completion in semantics
Topologies for the digital spaces Z2 and Z3
Computer Vision and Image Understanding
Closure operations for digital topology
Theoretical Computer Science - Topology in computer science
A digital analogue of the Jordan curve theorem
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Convenient Closure Operators on $\mathbb Z^2$
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Jordan curve theorems with respect to certain pretopologies on Z²
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A jordan curve theorem in the digital plane
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Graphs with a path partition for structuring digital spaces
Information Sciences: an International Journal
| Hi-index | 5.23 |
We study a special topology on Z^2 and show that both the Marcus topology and the Khalimsky topology and also one more digital topology on Z^2 may be obtained as three of its quotient topologies. A quotient closure operator of the topology studied is discussed, too, and an analogue of the Jordan curve theorem for this closure operator is proved.