A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

• Autorzy: Yang Z.
• Języki publikacji: EN

Abstrakty

EN

This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.

Słowa kluczowe

EN

proximity spaces

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 88, nr 1-2
• Strony: 207--223
• Opis fizyczny: bibliogr. 18 poz.

Twórcy

autor

Yang Z.

• Department of Mathematics University of the Incarnate Word 4301 Broadway, San Antonio, TX 78209, USA,

Bibliografia

• [1] Adàmek, J., Herrlich, H., Strecker, G. E.: Abstract and Concrete Categories, The Joy of Cats, John Wiley and Sons, New Work, 1990.
• [2] Chaudhuri, B.: A new definition of neighborhood of a point in multi-dimensional space, Pattern Recognition Letters, (17), 1996, 11-17.
• [3] Čech, E.: Topological Spaces, Interscience,Wiley, New York, 1966.
• [4] Efremovič, V.: Infinitesimal Spaces (in Russian), Dokl. Akad. Nauk SSSR, (76), 1951, 341-343.
• [5] Engelking, R.: General Topology, Heldrmann Verleg, Lemgo, Germany, 1989.
• [6] Herrlich, H.: A Concept of Nearness, General Topology and Application, (5), 1974, 191-212.
• [7] Hošková, C.: Various approaches to a proximity relation on a set, Acta Avionisa, IV(6), 2002, 38-41.
• [8] Ivanova, V., Ivanov, A.: Contiguity spaces and bicompact extensions, Izv. Akad. Nauk. SSSR, (23), 1959, 613-634.
• [9] Kelley, J.: General Topology, Van Norstrand, 1955.
• [10] Latecki, L., Prokop, F.: Semi-proximity continuous functions in digital images, Pattern Recognition Letters, (16), 1995, 1175-1187.
• [11] Lodato, M.: On Topologically Induced Generalized Proximity Relations, Proc. Amer. Math. Soc, 15(3), 1964, 417-422.
• [12] Naimpally, S., Warrack, B.: Proximity Space, Cambridge University Press, London, 1970.
• [13] Pawlak, Z.: Rough sets, Int. J. Computer and Information Sci., (11), 1982, 341-356.
• [14] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning aboutData, Kluwer Academic Publisher/Springer, Dordrecht, 1991.
• [15] Peters, J. F., Skowron, A., Stepaniuk, J.: Nearness of Objects: Extension of Approximation Space Model, Fundamenta Informaticae, (79), 2007, 497-512.
• [16] Ptak, P., Kropatsch, W. G.: Nearness in Digital Images and Proximity Spaces, DGCI 2000, LNCS 1953,, 2000, 69-77.
• [17] Riesz, F.: Stetigkeitsbegriff und abstrakteMenge, Internat. Congress Mathematicians IV, 2, 1909, 18-24.
• [18] Wolski, M.: Approximation Spaces and Nearness Structures, Fundementa Informaticae, (79), 2007, 567-577.