Digital topology aims to transfer concepts from classical topology (such as connectivity of objects, properties of their boundary and their neighborhood, as well as continuity) to digital spaces (such as Ζ2), which are used to model computer images. It has two main approaches graph theoretic and topological. Graph theoretic approach depends on 4 and 8 adjacencies which imply connectivity paradoxes. Our goal is to construct supra topological structure using 4 and 8 adjacencies to define connectivity to help in solving connectivity paradoxes. We construct 4 and 8 supra topologies. Properties of closure and interior operators are given. Examples and counter examples are obtained.
[1]
A. M. Kozae, Mathematics Department - Faculty of Science, Tanta University, Tanta, Egypt.
[2]
M. Shokry, Physics and Mathematics Engineering Department-Faculty of Engineering, Tanta University, Tanta, Egypt.
[3]
Mai. Zidan, Physics and Mathematics Engineering Department-Faculty of Engineering, Tanta University, Tanta, Egypt.
Digital Topology, 4 and 8-Adjacency, Supra-Topology, Digital Spaces, Closure Operator
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