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Grill Determined L-Approach Merotopological Spaces

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The present paper is devoted to the study of grill determined L-approachmerotopological spaces. The category having such spaces as objects is shown to be a topological construct (its initial and final structures are provided explicitly). The lattice structure of the family of all these spaces is also discussed. In the classical theory, this category (that is, when L = {0, 1}) is a supercategory of the category of pseudo metric spaces and nonexpansive maps.
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1--12
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Bibliogr. 35 poz.
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Bibliografia
  • [1] Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories, Wiley-Interscience Publ., New York, 1990.
  • [2] Artico, G., Moresco, R.: Fuzzy proximities and totally bounded fuzzy uniformities, J. Math. Anal. Appl., 99, 1984, 320-337.
  • [3] Bentley, H. L.: Nearness spaces and extension of topological spaces, in: Studies in Topology, Academic Press, New York, 1975, 47-66.
  • [4] Bentley, H. L., Herrlich, H.: Merotopological spaces, Appl. Categ. Struc., 12, 2004, 155-180.
  • [5] Gierz, G., et al.: A Compendium of Continuous Lattices, Springer, Berlin, 1980.
  • [6] Hassanien, A. E., Abraham, A., Peters, J. F., Schaefer, G., Henry, C.: Rough sets and near sets in medical imaging: a review, IEEE Trans. Inf. Technol. Biomed., 13(6), 2009, 955-968.
  • [7] Herrlich, H.: A concept of nearness, Gen. Top. Appl., 4, 1974, 191-212.
  • [8] Ivanova, V. M., Ivanov, A. A.: Contiguity spaces and bicompact extensions of topological spaces, Izv. Akad. Nauk. SSSR Ser. Mat., 23, 1959, 613-634.
  • [9] Katětov, M.: On continuity structures and spaces of mappings, Comment. Math. Univ. Carolinae, 6, 1965, 257-278.
  • [10] Khare, M., Singh, R.: L-guilds and binary L-merotopies, Novi Sad J. Math., 36(2), 2006, 57-64.
  • [11] Khare, M., Singh, R.: L-contiguities and their order structure, Fuzzy Sets and Systems, 158(4), 2007, 399-408.
  • [12] Khare, M., Singh, R.: Complete _-grills and (L, n)-merotopies, Fuzzy Sets and Systems, 159(5), 2008, 620-628.
  • [13] Khare, M., Tiwari, S.: Completion of approach nearness spaces, submitted.
  • [14] Khare, M., Tiwari, S.: Approach merotopological spaces and their completion, submitted.
  • [15] Kim, Y. -C., Min, K. -C.: L-fuzzy preproximities and L-fuzzy topologies, Inform. Sciences, 173, 2005, 93-113.
  • [16] Latecki, L., Prokop, F.: Semi-proximity continuous functions in digital images, Pattern Recognition Letters, 16, 1995, 1175-1187.
  • [17] Leseberg, D.: Symmetrical extensions and generalized nearness, Note diMathematica, 22(3), 2003, 93-111.
  • [18] Liu, Y. -M., Luo, M. -K.: Fuzzy Topology, World Scientific Publ. Co., Singapore, 1997.
  • [19] Lowen, R.: Approach spaces: a common supercategory of TOP and MET, Math. Nachr., 141, 1989, 183-226.
  • [20] Lowen, R.: Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press, 1997.
  • [21] Lowen, R., Lee, Y. J.: Approach theory in merotopic, Cauchy and convergence spaces. I, Acta Math. Hungar., 83(3), 1999, 189-207.
  • [22] Lowen, R., Robeys, K.: Compactifications of product of metric spaces and their relations to Čech-Stone and Smirnov compactifications, Top. and its Appl., 55, 1994, 163-183.
  • [23] Lowen, R., Sioen, M., Vaughan, D.: Completing quasi metric spaces: an alternative approach, Houstan J. Math., 29(1), 2003, 113-136.
  • [24] Lowen, R., Verbeeck, C.: Local compactness in approach spaces I, Internat. J. Math. Math. Sci., 21(3), 1998, 429-438.
  • [25] Lowen, R., Verbeeck, C.: Local compactness in approach spaces II, Internat. J. Math. Math. Sci., 2003(3), 2003, 109-117.
  • [26] Lowen, R., Windels, B.: AUnif: a common supercategory of pMET and Unif, Internat. J. Math. Math. Sci., 21(1), 1998, 1-18.
  • [27] Naimpally, S. A., Warrack, B. D.: Proximity Spaces, Cambridge Tract, No. 59, Cambridge, 1970.
  • [28] Peters, J. F., Ramanna, S.: Feature selection: near set approach, Lecture Notes in Computer Science, 4944, Springer-Berlin/Heidelberg, 2008, 57-71.
  • [29] Peters, J. F., Wasilewski, P.: Foundations of near sets, Inform. Sciences, 179, 2009, 3091-3109.
  • [30] Smyth, M. B.: Quasi-uniformities: reconciling domains with metric spaces, Mathematical Foundations of Programming Language Semantics, 3rd Workshop, Tulane 1987, Lecture Notes in Computer Science, 298, Springer-Verlag, Berlin, 1998, 236-253.
  • [31] Srivastava, P., Khare, M.: On lattices of fuzzy basic proximities, Indian J. Math., 34, 1992, 233-245.
  • [32] Srivastava, P., Khare, M.: Fuzzy f -proximities, Fuzzy Sets and Systems, 59, 1993, 197-203.
  • [33] Srivastava, P., Khare, M.: A note on classical and fuzzy f -proximities, Fuzzy Sets and Systems, 68, 1994, 239-241.
  • [34] Srivastava, P., Khare, M.: Fuzzy grills, fuzzy ultrafilters and counterexamples, Simon Stevin, 67, 1993, 65-75.
  • [35] Vakarelov, D., Duntsh, I., Bennett, B.: A note on proximity spaces and connection based mereology, Proceedings of the International Conference on Formal Ontology in Information Systems, p. 139-150, October 17-19, 2001, Ogunquit, Maine, USA [doi: 10.1145/505168.505182].
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0010-0023
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