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Abdelkrim Latreche
Farhan Ismail

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Abdelkrim Latreche
Farhan Ismail

WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

The Applications of the Universal Morphisms of LF-TOP the Category of All Fuzzy Topological Spaces

AUTHORS: Abdelkrim Latreche, Farhan Ismail

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ABSTRACT: Finding the universal morphisms for a given category is considered as comprehensive study of the principal properties that this category can achieved. In this work, we build a category of fuzzy topological spaces with respect to Lowen’s definition of Fuzzy TOPological space [3], that we denoted LF-TOP. Firstly, we collected universal morphisms of TOP category, listed by Sander Mac Lane [7]. Second, we studied universal morphisms of LF-TOP. We found through this study that the properties of this category are a generalization to the TOP category properties and TOP’s universal morphisms are projections of LF-TOP’s ones. This shows the power of Lowen’s fuzziness effect on the ordinary topological space.

KEYWORDS: category, functor, fuzzy topological space, TOP-category, universal morphism.


[1] L.A. Zadeh, Fuzzy Sets, J. 8, 1980, pp. 338–353.

[2] C.K. Wong, Fuzzy Points and Local Properties of Fuzzy Topology, J. 46, 1974, pp. 316-328.

[3] R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness , J. 56, 1976, pp. 621–633.

[4] C.L. Chang, Fuzzy topological spaces, J. 24, 1968, pp. 182–190.

[5] M. M. Stadler, M. A. de Prada Vicente, Strong Separation and Strong Countability in Fuzzy Topological Spaces, J. 43, 1991, pp. 95–116.

[6] C.K. Wong, Fuzzy Topology: Product and Quotient Theorems, 45, 1974, pp. 512-521.

[7] M.L. Saunders, Categories for the working mathematician, University of Chicago Chicago, USA, 1991.

[8] S. Carlson, Fuzzy Topological Spaces, Part II (May 17).

[9] S. Nawaf El-Diafy, Comparative Study of Fuzzy Topology, A thesis submitted in partial fulfillment of the requirement for the degree of master of mathematics, Gaza, 2014.

[10] S. Eilenberg, S. Mac Lane, General theory of natural equivalences, 58 , Gaza, 2014. 45, 1945, pp. 231-294.

[11] A.Kandil, S. Saleh and M.M Yakout, Fuzzy Topology On Fuzzy Sets: Regularity and Separation Axioms, J. 2, 2012, pp. 70-83.

[12] A. P. Shostak, Two Decades of Fuzzy Topology: Basic ideas, Notions, and Results, 44, 1989, pp. 125-186.

[13] S. Demiralp, E. Guner, Some characterizations of hope group on fuzzy topological spaces , 6, 2014, pp. 111-121.

[14] D. Susha, T. Thrivikraman, Box Products in Fuzzy Topological Spaces and Related Topics, Cochin OCHIN University of Science and Technology, (2004).

[15] M. Stephen, N. Moses, A. Paul, S. Hezron, Normality and Its Variants on Fuzzy Isotone Spaces, 3, 2013, pp. 639-642.

[16] S. S. Benchalli, G.P. Siddapur, On the Level Spaces of Fuzzy Topological Spaces, 2, 2009, pp. 57-65.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #27, pp. 213-219

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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