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Vol.3 , No. 1, Publication Date: Jan. 21, 2016, Page: 1-10
 to digital spaces (such as Ζ<sup>2</sup>), 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.&picture=http://www.aascit.org/aascit/decorators/img/journal/940.jpg)
| [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 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.
Keywords
Digital Topology, 4 and 8-Adjacency, Supra-Topology, Digital Spaces, Closure Operator
Reference
| [01] | A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, On supra topological spaces, Indian J. Pure and Appl. Math. no.4, 14(1983), 502- 510. |
| [02] | A. Rosenfeld, ed., Adjacency in digital pictures, Information and Control, 26 (1974) 24-33. |
| [03] | [3] A. Rosenfeld and J.L. Pfaltz. Sequential operations in digital picture processing. J. ACM, 13:471-494, 1966. |
| [04] | [4] Azriel Rosenfeld, ``Digital topology,'' American Mathematical Monthly, Vol. 86, pp.621-630, 1979. |
| [05] | Efim Khalimsky, Ralph Kopperman, and Paul R. Meyer:"Computer graphics and connected topologies on finite ordered sets,'' Topology and its Applications, Vol. 36, No.1, pp. 1-17, 1990. |
| [06] | Herman, Gabor T. Geometry of Digital Spaces Birkh¨auser (1998) x +216 pp. 2, 3, 6. |
| [07] | Paul Alexandroff und Heinz Hopf. Topologie, Erster Band: Grundbegriffe der mengentheoretischen Topologie. Topologie der Komplexe.Topologische Invarianzstze und anschliebende Begriffsbildungen _ Verschlingungen im m-dimensionalen euklidischen Raum. Stetige Abbildungen von Polyedern, (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band XLV), Verlag von Julius Springer, Berlin, 1935. |
| [08] | Pavlidis, T., Algorithms for Graphics and Image Processing. Berlin-Heidelberg-New York, Springer-Verlag 1982. XVII, 447 S., DM 74, ISBN 3-540-11338-X. |
| [09] | R. Klette and A. Rosenfeld. Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco, 2004. |
| [10] | V.A Kovalevsky. Finite topology as applied to image analysis. Comput. Vision Graphics Image Process, 46 (1989), pp. 141–161. [SD-008]. 2. G.T Herman, D Webster. |
| [11] | V. Kovalevsky Geometry of Locally Finite Spaces. Publishing House Dr. Baerbel Kovalevski, Berlin. ISBN 978-3-9812252-0-4, 2008. |
