**AUTHORS:**Abdelkrim Latreche, Farhan Ismail

**Download as PDF**

**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.

**REFERENCES:**

[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.